Thank you very much. It's great to be back in Trieste actually. I realized I haven't been here for 11 years and just seeing Eddie Gava reminded me of the good old days in the 90s when I came here basically every year because I was one of the organizers of the spring school and have very fond memories of that and I also want to thank the organizers of the Exacter G conference for an invitation. It gives me a chance to meet some of the people whose papers I've been reading. Okay so the title of my talk is this and just a couple years ago I started wondering about UV fix points and I was actually led to it through some adventures in so-called higher spin ADS CFT correspondence which I'll mention very briefly and then actually with Simone Giombi who is an assistant professor at Princeton and a couple of excellent graduate students we've done a whole bunch of calculations. Some of them are not entirely original but I'll share them with you anyway. So this is the incomplete set of various papers and in the first part of the talk I mainly talk about the gross Neveau conformal field theory and then in the second part of the talk I'll be a bit more adventurous and talk about the ON model above four dimensions which is a somewhat less clear topic. Okay so the gross Neveau model it crops up a lot in particular in this conference in two so gross Neveau's original paper was in two dimensions and the idea was that it it's a kind of nice toy model for four-dimensional QCD in the sense that this coupling in two dimensions is asymptotically free. Just to explain notation I'll mainly work with four component the rock fermions for reasons that you'll see in a second so and it's asymptotically free but it's it doesn't give a CFT in the infrared because there is a dynamical mass generation. Now there is the physics is somewhat similar to the two dimensional ON nonlinear sigma model with n bigger than 2 and now we're interested in going slightly above two dimensions where both the ON and the gross Neveau models have weakly coupled UV fix points and then they essentially become conformal field series. Okay so just to remind you the beta function for the for the ON model there is this negative term this is for the gross Neveau model. There is a term which is negative for n bigger than 2 and n is for an F in our notation it's also the number of two two component Majorana fermions which is the minimal number of fermions so our n just basically measures the number of fermionic degrees of freedom. When this number is bigger than 2 you have a asymptotic freedom in 2D but then slightly above 2D you have a perturbative UV fix point and this was appreciated I think soon after the gross Neveau original paper and a bunch of people long ago developed two plus excellent expansions for various operator dimensions and then here are the answers you actually notice one interesting thing is that all the perturbative corrections vanish for n equal one this is just the bare dimension of psi and these are vanishing perturbative corrections and this is the bare dimension of sigma plus perturbative corrections so sigma is just psi bar psi so for n equal one something special happens to this model and I'll come back to this somewhere a bit later now there are similar expansions in the n sigma model with n bigger than 2 which is also asymptotically free but that model is a bit more complicated because there are infrared divergences in due to the scalar fields. Now a 4 minus epsilon so the upper critical dimension as you push above 2 the upper critical dimension is 4 and of course the ON sigma model is in the same universality class as the Wilson Fisher ON model which is just the 5-4 theory with ON and variant interaction and at 4 minus epsilon dimensions it has a weakly coupled Wilson Fisher now infrared fixed point and so using the two epsilon expansions the 4 minus epsilon and 2 plus epsilon one can actually derive excellent approximations to the critical exponents in D equal 3 they're not as excellent as the bootstrap values that Slava told us about yesterday but but they're nevertheless played a very important historical role and for example in Kleinert and Schulte-Frelinde's book it's done up to five loops and you get very good values and the field is still not standing still there is now a 6th loop apparently available so it's been a great way to approximate things even though the epsilon there is summation of epsilon expansion is of course a bit of a it's not an exact science but it still helps a lot now the gross Neville model so the question is what is the UV completion of the gross Neville model namely how do you flow to it from above rather than from below and the answer actually it's something I didn't know till I started working on related things and kind of guess the answer but it turned out that it was in the literature since 91 in fact Zenzhou's 10 and independently Hassen-Fraenz Hassen-Fraenzians and Kuti and Shen basically realized that it's just the Yuccava multi-flavor Yuccava model and now people often call it the gross Neville Yuccava model so you basically it has the same symmetries it has a it's renormalizable in four dimensions these are the two renormalizable couplings in four dimensions but now the difference is that as you go slightly before slightly below four dimensions these become now slightly irrelevant as opposed to slightly irrelevant so this model has it's a little bit harder to calculate with because there are now two couplings so you need two beta functions for two couplings and so these are the beta functions up to two loop order these were actually done in in a paper by Karkine and collaborators in 93 and we rederived them and rechecked them and so you see some interesting things like the appearance of the square roots and the fixed point values of the coupling and these are the couplings up to the order that we need and then you can derive the operator scaling dimensions so now sigma basically stands for psi bar psi in the gross Neville model you get this number then you get psi dimension and also another interesting dimension is the sigma squared operator so using the two again using the two expansions the four minus epsilon and two plus epsilon you can actually construct good values between two and four and now they actually two plus epsilon expansion is under a better control because they're annoying for a divergence is so so here is there is one thing you carry from the stock many of you know this already is this picture that so we have this interacting CFT which in D equals 3 is basically strongly coupled and non-perturbative it's wedged between two free CFT's you can either float it from so the directions of the flow lines are like this this is from UV to IR right this is so you can either start with the the usual gross Neville model is sort of this part so from the point of view of N3 fermions you have to add an irrelevant interaction and you get here but there is also a way to flow down to this model from the free CFT of N3 fermions plus one scalar and the nice thing is that so as you very dimension when D gets close to four this fixed point basically slides near here and you can do perturbations here in here here when you when D becomes close to two you can do perturbations here in here and of course D equals 3 is the desirable case but you have really very good control from from epsilon these two epsilon expansions and also one over N expansion is another a good thing about which there are many things known and here is an example of another quantity that we recently calculated and this is a completely new calculation it's the so-called CT the coefficient of the two-point function of two stress energy tensors it's determined by conformal invariance and here is the result of our sort of resummed epsilon expansions as a function of D it's a pretty interesting result because you see that actually so this is N times CT over CT3 minus one so when it dips below below zero that means that CT actually increases when you flow from the UV to IR and some people worry about whether CT always decreases under RG flow this is actually strangely enough violated very near very near two dimensions but in three dimensions it's not violated so it actually does decrease under the usual RG but then there is another measure of degrees of freedom which is essentially what Calabrese just talked about this morning it's related to a particular kind of entanglement entropy in two plus one dimensions of course he mainly talked about one dimension where there is no shape dependence but when you start looking in two spatial and one time dimension then you are on the plane and the simplest type of region is well people often talk about just the half plane entanglement entropy but more informative in a way is the circle namely you draw a circle of radius R and you compute the entanglement entropy between inside and outside of the circle and then there is the aerial law here is just a perimeter law that's a non-universal term and then there is a sub leading universal term which you often see denoted as gamma in the gap system it's so-called topological entanglement entropy but we started calling it F and for reasons that essentially in this case there is an amazing trick of calculating this so for this particular shape and in a conformal field theory you don't need the replica trick you can just map it using you can essentially map this region to the sitter space and think about it as a the sitter entropy and Euclidean the sitter is just a three-sphere so so this F is just minus the log of a partition function of the Euclidean CFT on a three-sphere so if you will it's a kind of trick that allows you to compute the entanglement entropy in a very simple way and so there is something that actually in the paper with the Jaffer is Puffer and Savdi we call the F theorem namely that when you flow from the UV to IR the F UV is bigger than FIR so this is what's called the F theorem in the three dimensions and it's believed to be a kind of analog of the zomologic of C theorem in two dimensions and the Carti A theorem in four dimensions and to flesh out this fact actually John B and I a couple of years ago considered this quantity in continuous dimension like in the spirit of how we consider the CFT in continuous dimension we can do the same on this for this sphere free energy then it's convenient to define this quantity sine pi d over 2 times log z the reason you need this something like this is because F actually blows up near even dimensions due to wild anomaly so for example in 4 minus epsilon dimensions you see like a 1 over epsilon pole and same in two dimensions it's really due to the fact that there is then a log R term there is a logarithmic term in radius of this region so when you kill this off you you find that the result is a is a completely smooth function of dimension so this F tilde thing looks like this so here is a result for free theory so what are the simplest CFTs in the world they're just a conformal a coupled scalar field or a massless fermion and these are the you have to trust me on this it takes a little while to derive these integral representations but you can recognize some familiar numbers for wild anomaly so for example this F tilde in even dimensions is just pi over 2 times the anomaly value and so you you see for example like you know for a scalar it's 190 and you indeed see pi over 180 the blue line is a scalar and the red line is the fermion and that's a completely smooth function of dimension it doesn't exhibit any features it seems to monotonically drop off as a function of dimension so now that that's the easy thing to compute just for free fields but then we did perturbation theory in in the interaction so for example for the Wilson Fisher model you just perturb by 5 to the 4 interactions and and you have to do integrals over the d-dimensional sphere this actually gets very hairy and but now there is software that allows you to do these integrals the really hairy part is that there are also in addition to the usual renormalization of coupling constant you also have to add one of our epsilon poles multiplying the Euler number like there is the so-called curve because you're in curved space so you have to you have divergences proportional to curvature squared terms anyways after many months of computation you get the following 4 minus epsilon expansion for the ON Wilson Fisher model actually up to epsilon to the fifth and and it's actually is amazingly informative when you look at the numbers you see that the leading interaction corrections are very small and and you essentially find that you find that for example for the 3d easing model at the interacting fixed point this f is only 2 percent lower than the than the free scalar so the easing model is just the 5-4 theory so you flow from a free scalar to this model I used to worry a lot like when we wrote this paper about that theorem over five years ago I worried how do you test this and for example what if like the easing model results overshoots and becomes negative which would be really bad too it turns out that it's extremely close to free field value and this is not too unusual because even the dimension of the five field that in at the easing fixed point is only like 3.6 percent away from free field value but this is even closer okay so so now we did the same thing for the gross Nebusse of T there is a four in this case there is nice four minus epsilon expansion and there is a nice two plus epsilon expansion so it's exactly the kind of thing that's the easiest to put a you basically construct polynomials that match onto the information both near 2d and 4d and these are the plots as a function of D for this f tilde for the f tilde minus n of the free fermion and you see that it's always positive so so this f theorem is satisfied not just in 3d but for all dimensions and it also matches onto a large n computation which is easy to do which I will not describe here okay so here is a summary of the results on 3d gross Nebusse of T's as a function of this number n of the fermionic components this is not entirely new I mean there are other related papers but I hope we did a more complete job actually there was a paper about n equal 8 just the other day by John Gracie and and collaborators who were actually a bit often one of their estimates but but so you these are the plots as a function of n this is n equal 2 3 4 and so on the values in this table you see that that large n everything matches on nicely to the large n results and now let me so so basically we've succeeded using this sort of traditional Rg just resumption of different perturbative limits to get some hopefully good information about this CFT and of course this can be compared with the exact Rg results and can be compared with conformal bootstrap results which I think the work is underway by conformal bootstrap there already was an interesting paper but I think there is more work underway and now let me talk about the special thing n equal 1 which is as I mentioned it's a very strange limit from the point of view of the gross Neveau model because if you take just the two component by Rana sidebar psi square it just vanishes so there is no way to write this model as a for formula theory but there is a way to write it as a Yukawa model so in this case the one of the formulation is just trivializes but there is still a Yukawa formulation okay and in this case actually it's a simple model for something people call emergent supersymmetry it's just an example of how in the IR there can be enhanced symmetry so this minimal 3d Yukawa theory for one two component my Rana and one to the scalar field was conjectured to have emergent supersymmetry I believe for the first time by Scott Thomas in an unpublished seminar in 2005 at KITP or maybe 2006 but somewhere around then but he never wrote the paper actually his slides are quite informative but I found them easier to read than some of the subsequent papers but but then so the amazing thing about this model is that the fermion mass is forbidden by the time reversal symmetry so all that you need to do to reach the CFT is a single tuning of the sigma field mass and then it's alleged that you're automatically getting a supersymmetric model so this could be an example of how something supersymmetry can show up not at LHC but in some sort of condensed matter system and indeed there have been some attempts to at a condensed matter realization at the boundary of a topological insulator so essentially you can take the UV Lagrangian to be this minimal kind of was a mean oh model in three dimensions for the n equal 1 super field and this is the bootstrap paper but they actually didn't have a particularly robust indication of this fixed point although once you look at it it's sort of an agreement with what I'm about to show you so now so what happens in this n equal 1 case then for as I said you cannot use two plus epsilon expansion at all it just trivializes all corrections is zero that just means that this models in two dimensions it's not a weekly interacting theory it's actually I'll show you what theory it is it's a well-known minimal model it's a strong still stays strongly interacting even in two dimensions but it is weekly interacting in four minus epsilon dimensions and one sign of things happening for good things happening for n equal 1 is that the square root actually equals 13 it's not some irrational number which turns out to be a lucky 13 and then you plug in this 13 and you see that the two couplings are actually related by a factor of 3 which is a sign of this what you see in the was a mean a model so it's consistent with emergent Susie relation and perhaps even more strikingly all the different looking dimensions start just differing by one half up to two loop order so this is in Scott Thomas paper he had like this part and it actually wasn't clear how he was even doing the form I you have to realize that this n equal 1 limit is a little bit formal because if you start in four dimensions with a myerana you have to kind of take half of a myerana but this trick works very well I mean it wasn't emphasized by anyone writing these papers before but we kind of once we started doing this we realized that this is what needs to be done and strangely enough it works perfectly you see these one loop and two loop corrections lining up so consistent with the Susie relation and it's nice that to see it order by order in epsilon expansion so of course it's tempting to conjecture that this is exactly true everywhere below four dimensions and it would be nice to test at higher orders in epsilon I'm sure and there are some expert experts who can do you cover theory at three loops and maybe four loops but we haven't done it and but we're fairly sure that these miracles will continue to hold now per day to D equal 3 gives delta sigma which is this value and it seems close to the bootstrap result properly interpreted but I think there is more bootstrap work on the thing is that when you do bootstrap you have to assume something about the dimension of the next operator and and where you are depends on what you assume about that we actually know what the dimension of next operator is from our epsilon expansion and if you look at that point in the curve it seems to agree pretty well but another amusing thing is this continuation to D equal 2 it gives an interacting super-conformal theory and it's actually just a tri-critical easing model which has a central charge now one of the beautiful things about this F quantity is that when you continue it to D equal 2 it literally becomes the central charge up to some factor of pi over 2 so we can using the extrapolation of F that they this quantity the sphere free energy we can figure out what the central charge of the model is and the epsilon the epsilon expansion just gives us point to 1 7 which is amazingly close to 1 5th which is the exact value sorry sorry this is for the for the dimension of sigma and for f over f scalar it's even closer it's 0.68 while C is 0.7 so one can track these operators from four all the way to two dimensions and and it looks like there is a set of models with emergence of persimetry everywhere in between okay other maybe any questions about this or yes I think they're pretty I think they're pretty close yeah yeah I there were yeah I may not know all the literature well enough but there were in particular estimates for unequal 8 for example in the paper by Harbutt and Janssen and we actually just recently checked that they're close to that although they they were also part of what they were doing is also like this G and Y model the gross Navier-Cawa and some use of that but yeah yeah I mean it would be really fun to compare I mean we have this table with the literature that we have found I think these tend to be in good agreement this unequal 8 is a rather special value which many people studied because it's supposed to be realizable and condensed matter okay so now so when N is large this is that's actually how I got into this stuff in the first place so Polio Kavanai conjectured in 2002 that essentially the special thing about these large N or N and G N model is that they have an infinite number of approximately conserved higher spin currents in the sense that in free fields they are exactly conserved and the flow makes them still does not destroy this conservation and it means that all the anomalous dimensions of these currents are of order 1 over N and that's just what you need to build an interacting sort of an ADS dual and D plus 1 dimensions so so there is something called Vasiliev theory in ADS 4 I should say it's a different Vasiliev from the one who did the the large N calculations in that model so so this is Misha Vasiliev and he wrote some beautiful papers in the early 90s on just higher spin gravity found some formulation in ADS 4 and by now there is a set of checks of this duality so so this kind of gives another motivation so by studying these models you're supposedly learning something about quantum gravity in ADS space but it's a rather special theory of quantum gravity which which contains all these higher spin fields in addition to spin to gravity field now so the ADS CFT relation for the dimension of the scalar operator versus the mass of the field is just this it's a very simple relation and you can have both basically both the delta plus and delta minus values for some negative values of M squared I should say that negative M squared in ADS space is not necessarily unstable it just has to be above the bright and loner Friedman bound this is a very famous result in ADS space the bright and loner Friedman bound and in this range you can take both of these dimensions and actually if you look in ADS 4 say for the gross Neville model there are two values delta equal one and delta equal two and one of them corresponds to interacting theory and the other one to free theory so so this is and the same thing happens for this for this interacting oil model so it's a very promising thing to start comparing the 1 over n expansions so now I'm going to make a transition to something a bit more speculative like the the gross Neville model is like it definitely makes sense I think and it makes sense for all values of n and hopefully there will be more experiments yeah we've also done work on QED 3 which there is still a question whether it's a CFT for very low values of n but but there is a similar story at large values of n but then so you build the 1 over n expansion by using the Hubbard-Stratanovich auxiliary field for example in the ON model and this you ignore at the fixed point that's the sort of old method of which I don't know who applied it first maybe Ken Wilson but then it was really pushed forward by Vasiliev and collaborators and in the Leningrad group and so so you get like this the nice thing is that you get a non-local effective action for the Sigma field and there is a kind of induced dynamics you see the this non-local propagator emerging and then when you transform it back to position space you see that the Sigma field has dimension to up to 1 over n corrections which is the right value of dimension and then you can build the 1 over n expansion for the dimension for example of the Phi field just to make it clear now I'm talking about the ON model I'm no longer talking about the Gross Neville I'm talking about ON model so the dimension of the Phi field will have the free value plus 1 over n 1 over n squared corrections and people persevere to compute these functions as a function of D like so you know for example this eta 1 here is its explicit form as a function of D so it's a kind of non-perturbative thing where it it requires a certain diagram resummation and it's actually known up to order 1 over n cubed where it starts the formula get like half a page long and they involve all sorts of special functions and in fact some of these old papers on top of everything had typos and so it's a bit of a take some work to get into this field it took us quite a while to sort this out but one of their big tests was that you can compare with for my for minus epsilon expansion sorry okay so so here is something that is evident in this result even for the leading 1 over n so if you plot this as a function of D this is what you see it's positive between 2 and 4 and if it once it goes negative you clearly see that the large n series non-unitary because because this this is just the unitarity bound right so if this is becomes negative then you know for sure that a theory at very large n is already non-unitary but luckily it's clearly positive here and of course we all know that Wilson Fisher series unitary and nice between 2 and 4 but then it's again positive between 4 and 6 and then above 6 it really goes non-unitary and the two-point function coefficient C is has similar properties and we actually for reasons of this studying higher spin theory we wanted the 5d theory to be sort of okay like to still be at least unitary at large n and this is actually how we started worrying about the five-dimensional n model so so we started thinking could there be actually some kind of ON model formulation between four and six dimensions which is at least at large n unitary and at first it seems a little crazy because like you open Michael Paskin's quantum field theory book and he immediately tells you don't look for scalar theories above four dimensions they're all trivial right so you would need some kind of a UV fix point of this model but then when you start doing actually I didn't find it myself but Parisi told me that he wrote the paper in 75 on non-renormalizable interactions and literally discuss this model and this is sort of an old topic like if you go to four plus epsilon dimensions you see that there is a UV fixed point but it's at negative coupling and negative coupling it seems weird but it's not deadly at large n right you you can have a theory sort of sitting at the top of the potential at large n and still be sort of okay so our goal was mainly to study the theory in five dimensions because there is some indication of the existence of of higher spin theory in ADS6 which would be due all to this five-dimensional theory and then we started sort of thinking about what could be the UV completion of this this non-renormalizable theory and arrived at this and this we did independently for what it's worth I mean I don't think it's very profound but we we haven't found literally papers on this so it's surprisingly so it's just a version of our own symmetric cubic scalar theory and by quite analogously to the gross Navier-Cawa model you have to add an additional scalar field and write a model with sigma phi i phi i term and sigma cube term actually we realized this before we even knew about the gross Navier-Cawa model but and then we started playing with the beta functions so this was about two and a half years ago or more we started playing with the beta functions and we saw that there is an ir stable fixed point there is a real solution in six minus epsilon dimensions provided n is very large so so if n is above 1038 there is a solution if n is below 1038 it goes complex which is a pretty so if you draw the two like there are two curves that intersect when n is bigger than 1038 and and so this is the IR fixed point of this cubic theory but then the intersection disappears and that's a pretty typical situation that you can encounter like the there are two fixed points that merge when n hits this critical value and then they go off to a complex plane and they but it's sort of nice that for large n everything matches with the large n philosophy because there we could use just this large n philosophy and if you look at the so then you can do all sorts of perturbative checks with large n and they all agree and I should say that the the model is quite different from the original five cube model in six minus epsilon that Michael Fisher studied in 78 he studied the n equals zero version in that case the fixed point set at an imaginary value and that was manifestly non-unitary but stable manifestly non-unitary but it's actually stable because the past integral just oscillates and he did it he managed to estimate the liang edge singularity by continuing from six to two dimensions and this was before the exact solution of beloved Palakov's homologic was known so so this this was a kind of historic paper and but then we realized that there is a totally different sort of thing where n is large and the solutions are real and then we did the three-loop analysis the beta functions get complicated but then the nice thing is that we can match the six minus epsilon expansions of because you see you you know these in arbitrary dimension from the work of of a serial at all and you and you see that our six minus epsilon perturbative expansion exactly reproduces these so if you will it kind of gives you a new cross check on both the large n formula and the fact that the series is like the uv completion of the online model and then John Gracie did it even at for loop and it continues to work so so it's pretty non-trivial checks because you can compare many many coefficients here you can go like so the large n formula work to all orders in epsilon our formula work to order epsilon cube but to all orders in one of our and then you can compare the between some set of the two coefficients but then the question is could there be what happens in 5d and that of course gets non-perturbative and then one can try to do exacter g or some other approaches or one can try to resound the epsilon expansion and if one just naively proceeds by computing one of epsilon corrections you do see that 1038 gets corrected downwards twice pretty sizably by the two epsilon correction so if you just plug in epsilon equal one you you get down to a fairly low value but then John Gracie's value I didn't show it here is positive and largest so it's basically hard to tell but there is a kind of elephant hiding in this closet which is does it even make sense to talk about critical n for this model because it's just a cubic model right so so the path integral is not maybe strictly well defined so does the theory makes sense non-perturbatively so we actually did some work on this but never so far haven't written it up but we believe that at least the vacuum at at 5 equals here and sigma equals here is metastable because you can use standard instanton methods to compute tunneling like when you're in six minus epsilon dimensions you can just do perturbative Rg and the potential should be close to to the bare potential and the potential just looks like this right it's just looks like this so you to compute tunneling you need an instanton that goes from here to here and it's not hard to get this exact solution in fact it's in a paper by Alan McCain from long ago but we had to adapt it to this large n setting and essentially you find that the model is at least metastable with a long lifetime when n is large and epsilon is small so the danger is that you can pick up imaginary parts due to this instanton of order e to the minus n over epsilon but we haven't fully finished this project so we don't know for sure that these imaginary parts really spoil the game and then there was I guess we will hear in the next talk about some of the work from exact Rg which also suggests some possibly metastable solution and then there was some work from conformal bootstrap directly in 5d and it's fairly recent paper and it actually looks fairly encouraging for the existence of some model and five dimensions so they look that n equal 500 which is about half the value the critical value in 6d and they get these islands the type of islands that Slava reviewed in his talk that are definitely there and decree and shrinking for the equal 30 n model so you get similar types of islands and the large n result which is the only thing you can easily do for this model sits right in the middle of this island so so it looks like this these islands are kind of shrinking around what where you think the scaling dimension should be according to the large n approximation it would be very interesting to pursue this further and see if this is if these islands keep shrinking and how precise this is okay so so so the so let me conclude so I've talked about some adventures in in what seems to be the method of yesteryear which is time honored method this was long before my time in the field but I was told that the Wilson Fisher paper was quite a breakthrough because it gave a kind of quantitative tool to to approximate series and it happened to work very well for the ON model granted it doesn't always work very well but but it appears to continue to work well for gross Neveau model our paper also considered the Nambuyon-Alesinio model which is similar to gross Neveau but it has an extra U1 symmetry and then there are other vectorial CFTs to which one can apply it so why is this useful well Slava quoted my friend Poliakov saying that RG is a human-made thing but I mean it's good it was made at some point so it's certainly you know it's hard to be no for sure outside perturbative region but and you can miss some theories but when it works well it really tells you where the theory is and then this is for example a sign of like so here the RG tells you that this is where the theory is and so in the cases so far where bootstrap was successful it does agree with RG at least in almost all the cases maybe bootstrap gives more precision so I think these studies of RG give you a way to pinpoint where the theories might be and facilitate the life of people doing bootstrap because they can tune things to to find these theories more precisely I also talked about the RG inequalities like C theorem I theorem and F theorem they all give you a quantity which if a CFT if a short distance CFT flows to a long distance CFT something is supposed to decrease now in two dimensions I'm allergic of proof then in 87 that I vaguely remember first it wasn't clear how much of a breakthrough it was but it kind of set the gold standard for for these theorems and then for a theorem there is a conjecture by Cardi from 88 and then a recent proof by Kamorgotsky Schwimmer for F theorem there were conjectures a few years ago by our group and by Rob Myers and then was proved by Cassini and Huerta and now what I showed to you is a kind of possible interpolation between all these theorems just by studying spheres and continuous dimension because all these theorems actually come from spheres and continuous dimension and you can interpolate from A to F using this these sphere calculations and and also like these these things are useful for ADS CFT were in addition to gravity under higher spin fields now some small values of N can be very special because they're enhanced infrared symmetries for example for Yukawa CFTs one can exhibit emergence of per symmetry in the gross Neville Yukawa model one sees it for minimal number one myrana fermion we also have results what they're also not fully ours but revisited by us a two loop order by where you take a complex scalar and and a Dirac fermion and then you have more control because there is a kind of you want our symmetry so you can see these emergent symmetries for low values of n and then more speculatively we found a possibility of our n models and deep between four and six which I believe are at least metastable and what does it mean no one is completely sure yet but I think one possible interpretation is that that there are small imaginary parts to the scaling dimension which means that there is no true second-order phase transition but the transition could be very weakly first order and if that's the case maybe that can be seen in actual simulations so so there have been other approaches to the 5d and model other than our attempts to do it via epsilon expansion namely conformal bootstrap and exact Rg and I'll just end with a question like could the phase transition and 5d be very weakly first order for large n I don't think anyone really simulated and very large for on magnets in five dimensions but I think if we are right that there is some kind of metastable theory maybe that's what happens but okay thank you for your attention


with him, you know, but he was, I don't think he feels that way anymore now that he's like real pissed at the guy, but you know, like I think there are a lot of fans who kind of want to see this man redeem himself, but at this point he is just going further into the extreme.  Because if Maddox wins the lawsuit, then it normalizes that it's okay to just make these spurious lawsuits against people like poor people and people who are like fans of yours.   Everyone's fucked. This is the unfortunate thing. Like nuclear gas bomb, you gotta really think about this name, nuclear. There's a reason we don't use nuclear bombs, mutually assured destruction. And that's kind of the direction we're heading and not that Dick's going to be destroyed, but that like the results of this becoming a war is that Dick is not nice about it anymore and doesn't care what happens.  Like if someone sues me for this amount, they are not a human to me anymore. They're just someone who needs to die. So I understand why Dick is taking this approach, even if it's, even though like honestly, the lawsuit is such a joke that it's obviously going to fail, but the fact that it's costing everyone so much money is enough that like people are just, so now everyone's dog piling on Maddox. And this is where we're at right now is that because of this lawsuit, because when money gets involved, everyone reports on it. This is like, this is why kick starters when they get big always get reported on by like Homestuck was suddenly talked about in mainstream media when the Kickstarter happened, you know, like, cause when people see $2 million, they're like, whoa, what does that mean?  Everyone's got Maddox slam pieces. Everyone's got, now there is some interesting stuff. There's this guy called Rakita something. I don't, I haven't actually watched his videos, but I've heard they're really good where he just, he's like a lawyer who goes through the lawsuit and just explains in detail why it is so fucked and so badly written and why it will not work. But so like, if you watch Rakita's videos, you're probably confident that Maddox is not going to win this lawsuit.  A lawsuit is like a years long process. Now, the drama from this is kind of, I mean, obviously this is still looming over everyone's heads, but the drama has kind of dwindled a little bit because we all know the state of affairs. There's a lawsuit. It's kind of been this way for a few months.  No one's happy about it. But this is where we are. And yeah, hopefully it doesn't get any worse than this.  Oh, definitely. Because it's just kind of like, I do kind of side with dick, but regardless of who you side with, it's sad and uncomfortable because it's real people's lives that are being destroyed. Maddox and dick, they're both getting constantly harassed by each other's fans. Both of their lives have been affected.  And now I listen to it. And now there's a $400 million lawsuit hanging over the thing.  Yeah, especially when Asterios gets on, because Asterios, who by the way, works for one of the biggest ad companies in the world and is a genius at marketing, will really lay in that this is all depressing and horrible that Maddox has ruined his life.   Asterios, not so much, he doesn't care. He'll just come in and like cry over it.  That's pretty funny. But yeah, that's pretty much it.  Like, obviously when something big happens, there's gonna be like a whole episode talking about it. But for the most part, these are all just like running stories that you kind of keep up with. And there's little updates here and there, little bits of new goss, you know, that are floating around the sphere.    But you can listen to the whole thing, it can be fun. It's long as fuck, you're gonna end up behind. Honestly, I had to catch up to like, I had to watch like 10 episodes of catch up for this over the last week. And I had to be watching like nonstop all day to catch up on just 10 episodes cause they were all two and a half to three hours long.   They just established their own cryptocurrency, dickles. So there's still weird fun stuff going on in the show. You don't gotta pay attention to the goss but it's a huge part of why the show has been successful. Which I apparently have, but I don't because I don't understand cryptocurrency. Someone please explain it to me. Where are my dickles? He need my dickles. So in one thing, there was a great quote from Dick about this that I really love where he justified the, like putting so much emphasis on the drama in his show. Because especially early on, a lot of people complained that the show was like too drama focused. And he was just like, I'm sorry that I've taken this story of two human archetypes having a classic battle of the ages, like a real human story and made sequential entertainment out of it every week, just like a real show. Sorry I did that. And I was just like, yeah, I mean that's what this is. The reason Dick is playing this up is because he understands that even though it's happening to him, that makes it even funnier to him. Like the fact that this is happening, he thinks is the funniest thing in the world. Even if this is shit, this is the funniest thing that has ever happened. And he'll insist that over and over again. He loves that this is happening. Because this is a story you can only get on the internet folks. Like this is crazy. This is all crazy. And that's why I'm doing a lecture on it. You've all been entertained for hours just listening to some other guy talk about it. That's how great of a story it is. So yeah, there you go. That's everything. Catch up with them both. They're both worth listening to. But again, you can skip a lot of the Dick show. It's up, I mean, it's long. It's real long, guys. That's it. See you next Tuesday. See you next Tuesday. I found the Dickles actually, hang on. Wait, wait, wait. There's my Dickles! Hey! Hey! Hey! What? I think I'm gonna go watch them because probably the universe right now, my friend. Hey!


What is going on ladies and gentlemen? We officially Hit a new all-time high. I was trying to set the stream up before we hit the all-time high, but While I was setting it up. We officially hit a new all-time high We ended up hitting 69,000 496 so depending which exchange you're looking on that's on by bit. Let's see on Binance 69,000 425 let's see on Coinbase What that high is 69,000 324 so depending which exchange you're looking on is gonna be a different price But we've officially I believe we've officially hit new all-time highs on every single exchange What is going on guys today is what day is today the 5th of March to about 10 a.m. Here Where I'm located and Man, it is crazy crazy day crazy time to be alive It's been a long time coming. I know a lot of people have been waiting about three years for this I know there's been people that bought potentially at previous highs and now they finally are either Well, they're finally in profit, right? Everybody is basically in profit at this point And man, I'm super excited. I'm super pumped about this So hopefully hopefully you guys have survived the bear market and are as pumped as I am So in today's video, we're gonna we're gonna in today's live stream We're going to just kind of be watching the price here For Bitcoin as it hits new all-time highs see what happens from here. I'm gonna be giving some potential trade setups and I'm going to be Analyzing Analyzing it overall to see, you know What where we might go from here? What could it potentially happen from here and what potential plays we could you could potentially set up from here? So we'll be talking about all those things and just kind of hanging out for a little bit and Watching bitcoins price here as it hits a new all-time high like it just did literally like five minutes ago So, yeah, it we're super pumped. We're super excited here and and I can't wait like I'm hoping that we continue I'm hoping to see $70,000 and beyond here today. That would be super super exciting Let me go ahead and Let me go ahead and post that I am live here on Instagram real quick and on Twitter, so just give me a few and Then we'll jump into the analysis if you're tuning in right now. Let me know what's up in the comments While I go ahead and Post this up on on social media real quick. I see Yannis in the comments. What's going on Yannis. Happy new all-time high Rivers what's going on? I know you've been here throughout the bear market. Oh, man. It is crazy guys. It is crazy Let me Let me see give me a few guys I'll put my camera here so you guys can see me as well while you're looking at the charts So we can watch it together. We're currently pick what bitcoins price is currently. I'm actually move my Camera so you guys can actually see bitcoins price. Hold on a second. There we go So bitcoins price is actually if it dropped back down. We're at sixty eight thousand six hundred right now Hold on a second it so we're currently sitting at sixty eight Five hundred just about give me a second while I post this up. Let me see where is it? Yeah, so so I expect a lot of volatility here for sure I'm expecting Nothing nothing less We already saw if we look at we're looking at the four hour right now. Let's let's zoom in To the 15 minute to see what what these what price has to look like in the immediate in the immediate Presence right we can see that once we hit an all-time high It went up as high as sixty nine four ninety six and then it instantly dropped as low as sixty seven two nineteen So yeah, definitely Expected I spoke about it in the discord that I expected lots of volatility Once we we cleared that all-time high now what we what we could potentially see here now that we tapped that all-time high is You know, maybe there's a lot of longs in that area and maybe the market tries to trap them and Push the price back down to kind of Pick up some liquidity down back down here in this in this range down here So that's something that we're gonna have to watch out for let's take a look at the Heat map here to see Let me see where is it? Let's look at the heat map to see Where the liquidity levels are? liquidation heat map So this is in the last seven days What the heat map looks like you can see that we've basically been taking out all the liquidity to the upside So the majority of liquidity right now liquidity pools are Basically at 60 K and all the way down to 55 K Are we gonna drop to 55 K? I mean, that's a that's a pretty big drop Let's look at the monthly on the monthly You can see all the liquidity is all the way down here at 50 K But remember this this the monthly chart lags behind a lot So, you know, just because it says 50 K doesn't mean that we're gonna go all the way down there to 50 K and Now let's look at the last 12 hours Let's zoom in a bit here and we can see Yeah, we can see that pretty much we took off we took out the liquidity to the upside now There's not much more liquidity to the upside, but there's not really any liquidity to the downside either On the 12-hour chart that's popping up here So, yeah price currently still still floating around $68,000 Let me post a link here real quick What was the link to this live? My internet is tripping right now on my phone. All right guys, let's see. What are we at right now? River says $100,000 by halving by the halving. Hey, that will be wild.  I might my conservative Estimate was 100 K By the end of the year. That was my conservative estimate in the beginning of this year But I mean at this pace, who knows man, this is crazy. This is literally crazy The zoom into the five-minute chart here see what's going on So now we're watching it on the five-minute chart so we can see What price is really doing in real time right now? I don't know what's going on my phone. There's no internet Let me connect to the Wi-Fi again Hmm. We need some celebration music here I'm trying I'm trying to find The thing with with YouTube you can't play any music That's What do you call it? Copy-written right can't find They don't have a There's no way that they don't have Like party a party type of thing, right? There's k-pop country pop deep focus Tropical band bangers is that maybe that's party music. Let's hear it See what tropical bangers sounds like Put up the volume. I don't know what uh, how much of bangers these are These are chill. These are like pretty cool Definitely not that. I mean you're chill, you know, but I was looking for more More party vibes leave this song for now as I Try to find some something All right, there's a little bit more party They're gonna put some celebration music man. We just hit all-time highs even though price is currently dropping right now Let's see what happens here. We're at the The fifty five minute moving average Just going on an Ethereum Ethereum went set up a new recent high as well 38 34 So it's what's the theorems all-time high. Let's let's take a look at the theorems all-time high Because the theorem is lagging behind But we're getting there. We're getting close. The all-time high is 4875 4875 guys, so we are officially of a little over a thousand dollars away From Ethereum's all-time high. So that's the next one. Look at this chart. I got a sneeze real quick. Hold on Excuse me Hmm dance workout. Let's see what this dance workout playlist is. Oh, there we go It's all basically like reggaeton. I didn't know Spanish music was Workout music. It says dance workout try different playlists That's too crazy That's that's chill Yeah, I haven't been able to find any any celebration music guys. Sorry And I would just we'll just jam to these right here Hmm So, let me see Where we at on Bitcoin where we've dropped to 67. Let's let's go back to the five minute candles here So it's definitely a lot of volatility right now in the market as we just set a new all-time high And I still haven't been able to post this Oh my god, my phone still have no internet still says no internet connection. I don't know what is going on here guys With my phone. I don't know if it's my phone over its Instagram. I don't know. Yeah, I have no internet No idea what's going on here Let's see So we have Allison says hello. How likely is it to reach 73 thousand dollars this week? That's a great question So if you guys have tuned in in the last few weeks, we spoke about $73,000 for Bitcoin being a target and the reason why Was due to a pattern that we saw here down a second because I'm gonna make a trade real quick All right, so I'm entering a trade here a small position here at $67,000 above it. So on the break here. We just broke So here at 67,000 See if I can catch a quick scalp here in the 67,000 range if we get a potential bounce here Because we're going to see a bounce here at some point as the market buys a dip. I'm sure We've gone as low as 66 400 right now So let's take let's take a look here at What I was talking about as far as 73 thousand dollars now How likely is it? I mean, there's a possibility, but there's really no way to know because we've just been on such a crazy trajectory and What I what I am suspect what I am suspecting is a pullback here after New all-time highs. So that's kind of what I spoke about today with my group But if we look at this setup here We can see it's pretty clear on the chart, right? If you look at it here, we're looking at the weekly chart We have this move up Let me remove let me clear let me clear the chart up a little bit here So I'm gonna leave this because this is gonna be a big love level here But I think we can remove this one here already So basically we had this move up I'm gonna remove these as well Let's clear things up a little bit here This is a the longer term Trendline that we have stayed above basically this entire time since we bottomed out Currently it's very far away. It's sitting at 30 35 thousand dollars basically right now Then we have this trend line currently that's sitting At about 45 thousand So both both those trend lines are very far away And of course the moving averages, but Like I was saying We had this bull flag here basically a both what's a bull flag a bull flag is when we have an impulse move We have some consolidation and pullback and we have a continuation, right? So how do we measure a bull flag? It's pretty simple And turn down the volume on the music it's pretty simple to measure a bull flag All you do is measure from the beginning of the bull flag getting of the move to the top Right, then you grab this and you put it where the breakout would happen which is right there and this gives us a Estimate a price estimate of about seventy three thousand dollars So that's that's basically how we got to that number. It's it's not exactly seventy three. It's seventy two Eight, I think let me see if it tells me if I click it seventy two thousand seven fifty four Is the exact number that it that it gives us? So that's how we get that that number there on the breakout so that's currently what we're watching here Can we get there this week? I Don't know. I honestly don't know it's such a big move already. We're due for a pullback at some point, right? When are we gonna get to get that pullback? I'm not sure. I'm I just hit so I just hit I'm taking profit here on the trade that I took What was it sixty seven point at sixty seven point five K and setting Tell stops so I just I just took profit on on that trade that I took at sixty seven thousand here at sixty seven thousand Five hundred so very small trade. I'm just looking to scalp these levels here on any any pullback So that's why I love when there's a lot of volatility because when it overextends to the downside There's almost always a bounce right back up from a small support. So I like to play big hole levels They're just simple to play And and we just got that bounce back up So I you know what I basically the idea is you take some profit put a trust up on it right around there So I had it usually around 200 250 dollars so if price goes back down I Troll out in profit and then if we go back down below Sixty seven again, and then price backs bounces back up above sixty seven again I might I'll consider taking another long trade there. So I try I've officially trialed out here at sixty seven Now I'll consider another long trade here, or I'll wait for a better entry so Just kind of updating you guys on my thought process as a as the price just kind of moves around here on the trade that I just took so Trilled out So I'm typing because I'm letting my my team know here as we As we do this in the discord if you guys don't know I do have a discord in the discord We provide all all types of things that I we I provide Either signals my personal signals that I'm taking like I was just talking about live with you guys right now I entered at sixty seven thousand took profit at sixty seven five hundred quick scalps So we do that We also have a Option singles so basically It's a way of making passive income by selling option contracts to option traders So I have a new video actually coming out on that this week that breaks it down because this is a Strategy that literally nobody in crypto is doing talking about or even knows about and it probably has One of the best returns on investment right now That I've seen because option traders are in in crypto are such they love to speculate crazy moves Which basically pays you they get they're giving you free money, right? It pays you premium. So Yeah, that that's that's probably the one of one of my favorite things to do right now in crypto and Have a video coming out on that this week And then we have the algo signals which basically it's an algorithm which Scans the market 24 7365 for trades with high probability setups with a hit rate of 80% or higher and And those you know it gives you the exact trade plan exactly what's going on And then the newest feature that we just added to the group is auto trading. So basically auto trading is it's taking The algo signals and automatically making all the trades for you. I'm testing it right now But it's it is already released. I'm testing it on an account with a thousand dollars. I'm already up on this account Let me see where it's where is it? So this is the The trader I have put a thousand dollars in it in in about two weeks. I'm up $200 That's a 20% return there guys in a matter of two weeks, which is insane I don't always expect 20% returns in two weeks, but it's it's been we've had a really really good run here in crypto and Obviously, you can see it as well in the auto trader And yeah, so if you guys are interested in any of that, of course, the link is in the description Because we have we have a lot of things that we've been working on guys And and by the way the option signals are hit rate our win rate right now in 2024 is 100% We have literally not missed a trade in options, which is why I love options This is our options right now just a quick spreadsheet Where I tracked all my trades there and you can see it's currently year-to-date. I've done about 62% return in two months guys We've done 45 trades this year. And if you notice we have zero losses 100% win rate So yeah, and it's been returning the last two months 23% 20 basically 23.98% 24% and already this month were up about 6% So this has been very very lucrative if you guys are interested in finding out more this week We have a video coming out on exactly how you too can Can do this can trade can sell options Let me see here timbers. What's going on timbers? Finally hit all-time highs. Glad to see you win here again Allison of course Allison Yeah, I know I didn't give you an exact answer. I don't know we're gonna hit 73 It's it's tough, right? I think once we break 70 then for sure We'll hit 73 probably pretty quickly within the week of of hitting 70 of breaking above 70 But I think we're still You know, we're gonna we might need some consolidation around this this area here So I was looking this morning. I was looking at the last time in the last bull run That we were at a previous all-time high. So that was back all the way back here Let me see In the 20 so is this a little area right here? Let's zoom Into the daily so we can see exactly what was happening during that time. Let's see where are we I'm lost No, I'm in the wrong year so it was way back here in 2020 right the end of 2020 beginning of 2021 We had the We were we were testing basically the previous all-time high from 2018 2017 right so This is the first time we tested it was right here at 19,000 for 48 and then net over the next two days You can see that we the market dumped and we actually dumped about 17 percent So let's take a look at that the high was there and the low is here. That's a 17% drop After testing the previous all-time highs, you can see that the we had a high of 19,565 I think the all-time high was around 20,000 and Bitcoin's price dropped about 17% after hitting that then over the next few days basically Price moved right back up. We consolidated and then we finally broke above the previous all-time highs And you can see once we broke above the previous all-time highs Bitcoin's price Really took off here. So let's see the day that we broke out was right here and We basically Bitcoin's price moved up about a hundred and sixteen percent throughout Basically the next month or so, right? We had a hundred and sixty sixteen percent move there where we went from the previous all-time high of twenty thousand dollars and set a new time high at that time of forty two thousand dollars Then Bitcoin's price consolidated. We you know pulled back once again You see we pulled back from that high to a low of What was the low here? 28,000 which was a 31% pullback and then after that 31% pullback Once again, we got a move Let's see how high this move went so we got then the next move here from 28,000 all the way up to 58,000 that was a move of another 100% move so Once that happened once again a pullback again 26% pullback and then after that We had a move up of About 44% setting a new all-time high of sixty two thousand So then we had that a pullback once again 18% pullback Then a move back to the upside and we set a new high at Wait, not this one that we didn't set a new high that time. So we went up to Where's a high there? Hold on. Oh Yeah, we did so sixty five thousand dollars was was that new high and Then we got a massive correction So we had from there to here that was a 27% drop And then from here if you go all the way to the bottom here of this correction, that was a Actually, this ended up being the bottom. That was a 55% drop All right, so And of course after that After we bottomed out there we got in one last move up Actually, we got a few moves up but the the the whole move was a hundred and forty percent But of course he came in chunks We went basically 48 percent Then had a pullback of about 12 percent Then moved back up 42 percent another pullback here 25 percent we set up a new high here at sixty six thousand dollars With a move of sixty nine percent had another pullback 13 percent pullback and the the final all-time high which we just broke today was of sixty nine thousand dollars so You know, I'm just kind of breaking that down so that we can have an idea of how the market moves Even when we're in a bull market and when we're setting all-time highs you can still expect a Lot of pullbacks, right? So if we kind of take a look at these pullbacks, I want to get an idea of What the average pullback was during this time? So let's take a look here So the first pullback When we hit when we initially reached that previous all-time high was 17 percent So let's put 17 Then the next pullback was 31 and a half Then the next pullback was 26 and a half pullback after that 18 and a half Pullback after that was 55 Pullback after that was 25 and then the final pullback ended up being About 13 13 point seven So how many pullbacks was that one two three four five six seven eight So divide it by eight So the average pullback ended up being about 23.5 so 23 and a half percent was the average pullback during that previous All-time high during the previous bull run there now What we have to account for is that usually every all-time high or every as as price progresses Bitcoin's price matures the market matures The pullbacks are less and less volatile So that's something that we've seen and now with the ETS a Lot of you have to think about it, right? Who's who's putting money into ETS? Usually older people are in the stock market Institutional investors aren't looking to get in and out in and out, right? They're looking a lot of times to put money in for a long term for the next few years because if you have a lot of money Ideally you want to hold your position a minimum of a year because if you sell before year Your tax a lot more your tax is a lot higher than if you hold for at least a year. So with that idea in mind And the inflows of the people there's so many people buying Bitcoin right now with through the ETFs Though the pullbacks might not be as volatile as before so Either way, let's take a look at what a 23% pullback would look like like where would that take us? so if we go over here and Look at a 23 and a half percent pullback that gives us a Price of about $53,000 What's going on Teddy got my dog here with it resting his head on my lap What's up, buddy? so he's very sad if Bitcoin's price were to pull back 23 and a half percent to $53,000. I can tell I can see it in his eyes how sad he is But I don't I don't think that's gonna happen because if we're thinking If we're thinking that pullbacks won't be as volatile Then You know, I'm not expecting a 23 and a half percent pullback even though that was the average, right? But but again, I'm still not expecting it last time we reached the previous all-time highs Remember, we did have a pullback during that time as well We reached the previous all-time highs. We didn't break them But we we got to that point and we pulled back about 17% so what would a 17% pullback look like? 17% pullback from the current highs would take us down to about about 57 58 thousand dollars 57 618. So that's more or more or less Where that would take us if we were to see that type of pullback So, I mean either way guys anything out what I would say anything But anything more than a 15% pullback. That's where you start to build some positions overall Even if you're doing what I've been doing lately And I covered a video about this. I did a video on this was Building big positions on any pullback beyond 15% so that's kind of like a little rule for with leverage though This is not like my long-term term portfolio. This is my Derivatives portfolio where I'm just as soon as it starts it gets beyond 15% I'm just starting to add to my positions and every time it gets even lower. I add a little bit more now I'm not taking a huge risk But this has helped me basically in the last when we get the last pullback I Ended up. I started buying around 42,000 All the way down to 38,000 that was around the bottom of that pullback and my average price ended up being around $41,000. I still had that position open guys and it's basically made me half a Bitcoin Just by holding it there So those are the type of things I'm looking to do because those are those can be very very lucrative during a bull run So during bull runs My the best suggestion that I can give is on any any pullbacks beyond 15% Start building up positions and as they drops more and more build more build, you know build up your position bigger And you can see if you would have done that last bull run just imagine Let's say you were doing a A You know 10 10x leveraged position, right? And let's say you didn't catch the bottom, but let's say somewhere in the middle is where you you would enter So let's say right there That would have been a hundred and forty five percent move if you're using 10x leverage. That's 1450 percent move Now if you did the same thing here This move was you know a hundred percent and so that would have been again a thousand 20% with leverage if you did it again here 44% 440% with leverage if you did it again here 28% 280% so so you get it right like you can make massive amounts of money With if you start building your positions Beyond a 15% correction and just hold them long term You know you could have now We're always gonna say We can't hit we're never gonna time the exact bottom perfectly We're never gonna time the exact top perfectly, but if you could have been somewhere in this even if you didn't Get a thousand four hundred percent if you if you hit half of that seven hundred and fifty percent That's insane right. That's an insane return on on any investment You know if you if you just put a hundred bucks on that and you got seven hundred and fifty percent return 750 dollars right on $100 investment so that's kind of kind of how you have to approach it There now you have to be wary of big drops like this So that's why you need to be sure that your positions aren't too big and that you can add more to your positions So that you your position doesn't get liquidated or to have some sort of exit plan If price keeps dropping like this Like we did in this scenario now. I think we're still really early in the bull run I wouldn't expect any massive massive corrections. Maybe something between 20 to 30 Will be would be realistic. I don't think we see any 55 60% pullbacks here at this time But just keep in mind. This is crypto. This is Bitcoin. It is volatile. It is high risk. So Anything could happen, right? So Yeah, if you guys have any questions about anything that we're covering here Make sure to drop it in the comments and I'll be happy to answer those for you guys Let me drink some water. Let me see if my internet is working on my phone yet Doesn't look like it. I don't know what is going on Let me disconnect from the Wi-Fi again No internet connection Wow Here my Wi-Fi back on So I might be an Instagram thing because it's let me see let me try some a different app Let's look at Twitter Twitter is working fine Let me look at My trading exchange That's loading perfectly fine That's trading fine. Yeah, everything on my internet is working fine and obviously I'm live streaming. So I Don't know I don't know what's going on my Instagram is not not working right now Let me check if it's If it's working here on the browser Yeah, it's working fine here. Yeah, I don't know what's going on. I'm not sure But at least my post got put up. All right, let's see. Let's see in the comments here. What's going on? Yana says Bitcoin went 0.2 percent above all-time high and immediately went down 3 percent. It looks like a trap to bulls Yeah, definitely. There's definitely a lot of people selling up there I wouldn't say a trap. I think this pullback could be a trap for anyone trying to short But because there's a hundred percent there's gonna be a lot of profit taking up there at at all-time highs, right?   They probably got liquidated by now. Let's see. Um Coinbase the Coinbase app how it's ranking So Coinbase. Okay guys, this is interesting Coinbase app is now The ranked number 44 In the app store overall and in finance apps It's number four so the reason this is important is because um In the previous bull runs whenever bitcoin topped off Or like peaked app was number one Was a number one downloaded app on Coinbase So something to keep an eye on i'll keep you guys updated on this right now It it just broke into the top 100 yesterday, I believe let me see to what days today today's the fifth So yesterday for the first time it broke into the top 100 overall downloaded apps currently is sitting at number 44 and in finance Apps it's number four. So That means there's still that means retail is definitely coming in but there's still room right is is not like it was last time So once it gets to number one, that's when we have to start being careful because that means retail is definitely like Aping in right When retail starts aping in that it catches that much um That bitcoin catches that much media attention and that many retail investors come in That's when bitcoin's price tends to drop. That's when we we tend to see big corrections. So uh, that happened Uh in 2018 That happened in 2020 and that happened twice in 2021 both when uh in may when we hit 65 000 and once again in november When we hit 69 000 so You have to be we'll have to be careful And keep an eye on that because that could be a signal or indicator You know that We're probably going to drop at some point soon So now one thing to to notice here on the daily Notice that we've hit a new high here In the price but the rsi Didn't hit any high. So remember that happened last time So if we look back here If you look back here We can see that the rsi was clearly trending to the downside While the price was clearly trending to the upside What happens there? That's a bearish divergence, you know, because rsi is a momentum indicator If momentum is trending down, but price continues up There's it's a it's a divergence, right? And usually when that happens. There's either a period of consolidation or a period of a pullback and we got that right we saw Uh during that time we saw look at all this consolidation and this pullback all the way down here We bottomed out and then continued to the upside So what happened here? Um once price right right in this area right here, let me see if I can Right here. That's when we finally broke out Which is about the same time where we broke out here and got that move to the upside, right? So now what's happening now Is that we're starting to see something similar? Right? We got Here was fine, right? So this was good rsi and price were perfect there. We had uh higher high We had higher highs, right? But now We're looking at these two peaks And we had From a high to a lower high So that could be the beginning of you know, that could be a sign that we're heading for some consolidation Or some sort of pullback now doesn't mean it's going to happen immediately because if we look back Look at when when this first happened that happened right here, october 24th And then uh november 1st, right? And if you go all the way back we could even look at november 10th where we set another new high So that's when those two peaks formed which is similar to these two peaks but Even after that Price continued to go on. So let's see. I would say that's around the november 9th And we we continue setting new highs all the way through Uh the 11th of january. So for two months, we bitcoin's price continued setting new highs while momentum continued setting lower highs so Just because this is starting to happen again here doesn't mean that Price is not going to continue to the upside. We can still continue to see price move up But it does mean that eventually at some point in time, we're going to see prices move back to the downside here So that's another thing that we're going to be keeping an eye on and of course, we'll we'll be keeping you guys updated As we continue to to see these things play out and as we continue to update you guys do these live streams and all that So it looks like bitcoin setting up some new lows is going lower here today Uh, we just hit 65,000. I think the low right now is What's the low 64? So we actually hit 64,986 I didn't even notice that that's crazy And we have big and we have um, sorry ethereum at 37 So let's see. Let's see what what happens here. I'm gonna take this out the way Let's go back into the five minute chart As we continue to set up some new lows here So how far could this pull back go? I'm not sure. I am not sure um So i'm looking for areas of support We have an area of support here around 65,000, which is exactly where we just hit recently Um after that we have another area of support here around 63,000 We got some support here again around the mid 62 Then at 62 we have some support 61.5. So it looks like every like 500 dollars We have we have minor and it's going to be minor areas of support, right? So if we zoom out a bit here And try to find uh, some potential support areas The biggest support is probably right here, which is right around 63 63k So um, let's highlight that area there actually So it's gonna be something like that Let's make that yellow So we can actually see it So that's a potential area of support If we want to look if we want to find more potential areas, we can pull up a Fibonacci um Retracement tool and run it from this area here from that first where the move first began to about the top Make this a different color And that shows us some potential support areas there as well. So now, um looking at that I can barely see this one. Why is it so Make it a little thicker. There we go All right, so now now it's giving us showing us some other areas of support. You can see right here. This is right around 65500 So that's a potential Support area there So we'll be watching We'll probably be watching those areas there for now to see what happens Well, like that that could potentially be a Good risk return trade there actually, let me see Trying to see where you would have to set up a stop Then the next Fibonacci area sits at 64,500 And then after that, of course, we fall down to this support area here that we spoke about So let's see. Let's see if this Fibonacci level holds up here It looks it looks like it held up throughout this candle held up here And now it's holding up here as well. So that could be a a good level there Yep, river says hit the like button everyone show the channel some support Yes, definitely guys make sure to to smash that like button make sure if you guys are not subscribed to the channel to subscribe to the channel Um today bitcoin if you just tuned in bitcoin just hit a new all-time high guys Uh, we're very very excited to see that So now the crazy thing is Instagram is not working at all for me Can you guys check on your end is instagram working fine for you guys? Let me know in the comments if your instagram is working fine for you I'm gonna pause my vpn and see if maybe that's what's causing it Once again, it's nothing And the crazy thing is on my web. It's also not loading Very very odd Hmm see Okay, so it's it's not it's not just me. Okay. I'm just making sure that it's not just me because I've had my account Suspended before and I wasn't sure if my if maybe that's why it wasn't working because my account got suspended So like two years ago, my instagram account got suspended It uh, and it was suspended for like two months And I have no idea why like there was there was no reason why it was suspended for um So I was hope I'll I'm just making sure that it's not just me all right, so we actually just uh Hit a new low here On bitcoin's price we went down to 64 400 So we're we're definitely getting a poll back here Let's see how low so so far the pullback's been about 7.3 percent so far But look how fast this is getting this got bought up that that new low Just got bought up super fast So we hit a low of 64 400 and we're already a thousand dollars. It bounced a thousand dollars instantly basically Yeah rivers, uh retail money's definitely gonna Start coming in soon it's You and you can you can pretty much tell by watching uh by by you know by the the rank Of coinbase app. Let's see coinbase is coinbase has coinbase crashed. I know yesterday was having issues So far looks good. It looks coinbase looks like it's up and running fine. Yeah coin coinbase looks like it's good Hmm Yana says rs also rsi is overextended in weekly time frame. Maybe we have to cool down a little in weekly time frame so um So remember Remember that rsi is a momentum indicator So what exactly does that mean it means that even if it's overextended It doesn't mean that price is gonna drop just because it's overextended So if we look at the weekly And we look at every time it's been overextended And then we put a time frame to it So it got overextend the most recent time it got overextended was back in october of 2023 And you can see bitcoin's price continued going up Basically until we didn't get back into into the Out of being over over what is it over bought over yeah over bought Until january 8th right so from october to january it was like that And then it you know cooled down a little bit as we consolidated here And then continued up and then if we keep going All the way back here. This was previous bull run. You can see in october 2020 We got into into over bought territory and that lasted until February of 2021 So how long was that a pretty long time? And you can see price just continued up like it went on a tear right so The rsi alone doesn't doesn't signal a You know whether price is going to go up or down It just kind of gives you an idea of where the momentum is and then But then when you pair it with for example with the price and you start comparing price to rsi Now you can see divergences. So now now that could start signaling some potential coming What do you call it consolidation or pullbacks? But the bigger the time frame the longer it takes for that to happen. So You know even here we had we had this bearish divergence here You know, but in the weekly it happened way before so I mean in the daily it happened way before So the daily is always a lot faster than the weekly which can give you, you know, kind of let you know ahead ahead of time Where where, you know price might be going So let's go back to the four hour chart here Let's actually go let's let's take a look at the five minute. See what's going on in the five minute So there's a five minute chart right now. I'm looking for anything bullish here If we get some sort of bullish candles, then I and I consider a Trade setup for a long. I would love to catch along to the upside here but Right now there. I don't see anything that that I would like here So we can see that we've got all red candles here This one here had potential Because that's considered a bullish pin bar But The next candle we've we've seen continuation here to the downside. So I'm not not going to play. I'm going to just stay out of the market for now Um, let's see what price does here how it reacts So just just going to hang out for now and uh, not not going to try to get into any position Just to get into a position, right? I want to see A reason if I want to see price really begin to bounce here I would love to see a bullish candle at this support here and then I can push to the upside then I'll consider, you know a position a potential scalp All right, so a lot of multiple people are saying that instagram is down. Okay, just making sure that it wasn't just me We have a River set is down Allison said it's down Yana said it's it's okay for him Teddy said it's down Timmer said it's down. Okay, so it's not just me then we're good then we're golden I wonder if uh, bitcoin broke instagram. What do you guys think? All right guys Yeah, I can't do anything On uh on instagram still down for me Let me connect back to my vpn then So i'm basically always on a vpn guys that that's like, uh I no longer turn it off at any time basically Since i'm always trading Or always looking at the exchange. Um, I have to just basically keep my vpn on at all times Um, the so if you're if you're looking to to use a vpn At first and if you're if you're not trading a lot then I recommend you find a free vpn The one that I was using for free was a wind scribe And for free it's it's not bad right? It's pretty good Especially if you're not constantly on the vpn then it's fine now What what I ran the problem I ran into is that I was Constantly constantly either having to turn it on and turn it off right because wind scribe since it's free You only get I think up to 10 gigs per month Uh for free right after beyond that you have to pay for it So if you don't want to be using the free gigs Then you had to constantly if you're not using it just turn it off um then when I when Even when I had it on like sometimes I forget leave it on the internet was super super super slow So um what I ended up doing I ended up, you know looking up the best VPNs basically and uh and the one with the best reviews was nord vpn So I ended up getting nord vpn And it it's it's been great. I basically have unlimited use for nord vpn and I don't notice a difference in My internet speed like at all like I watch videos. I could stream. I could Live stream not live stream, but I could watch live stream. I could watch whatever it is I want I could download things and I do not notice a difference at all With the vpn on so at this point. I just keep the vpn on at all times If you guys are interested, I do have a link for nord Just let me know and I'll post it. I don't think it's in the description. I should probably add it And I have to redo my description because I haven't updated in a while So that's probably something I should I should definitely be looking into Yeah rivers nord is amazing. I use nord I like I said, I use it for everything now. I literally Don't turn it off. I leave the nord vpn on at all times right now All right guys, so we got a a bullish candle here Should we and we were it's looking at we're getting a nice bounce I don't know if I want to enter at 66 Try to try to catch a scalp or if I should just just chill Right, let me see what my options are doing. So my options are definitely down because of What do you call it Because of volatility so so with options there's multiple factors that uh that go into Why you know what moves the the contracts value in an option And you could you could look up the greeks is basically what it is But the main factors are price so price the closer to your strike price that the price gets then You know the the lower the value or the higher the value of the contract goes so if it's higher Uh a higher value than for me since I'm selling it. I'm not buying it. It's worse for me Um The other thing is volatility. So right now because there's so much volatility in the market The premiums and the value of the contract goes way up, right? So when I so even though my my strike price is at $60,000, which is nowhere near where current prices are Because of this volatility here Um, you know, I'm I'm in a I'm in the red right now. So All I got to do basically is wait, right? Waiting is all there is to the game So as now as time is another major factor in option contracts So the closer and closer we get to the expiration date of my contracts The the more money I get and the less value the contract has Or the the contract gets as long as it's not close to my strike price So even if by my strike price, uh, the the price of of, uh, bitcoin gets To like $60,000 or just above it. I'm still fine and I'm gonna make all my money. It just can't go below it so, um Yeah, so right now, you know, I'm still in the clear 6500 we're $5,000 away from the strike price So I'm still good, uh, and I have another I think I actually have I just remember to have another position that I opened at 62 So even at 62, we're still good. It's a friday expiration date for that one the 62 I feel pretty good about it. Um, can it drop another 3000? It definitely can. Hopefully it doesn't And the reason I put it at 62 is because when I zoomed out, I saw this big support level here that uh, that we drew out So this uh, where is it this support right here? So this is at 63 So from 63 to 62, it's a pretty big level of support there Can it drop below it? Of course it can, you know, anything's possible And if it were to get to that point, then I I'd be looking at that point to close out the contract and just kind of roll it back Take any small losses at that point and just make it back in uh, in a further expiration date So that's pretty much how I play it But hopefully it doesn't come to that. Um, I haven't had to worry and I haven't had to worry about anything like that happening So far in 2024 I haven't had a loss since the 13th of december. So hopefully it doesn't come to that But we will wait and see what happens here. Let's see, uh rivers, um So if you're looking to get back into it, uh, I'm using so I'm still trading on buybit mainly However, for buybit, you do need not only just a vpm, but you're also going to need An id basically that's not in the us So, um, I I had to get in an id Basically outside of the us, uh, it's called a digital passport And I can share the that website with you if you're interested It's about 250 bucks a year you get a digital passport in that's in the republic of palau or palu I don't know how to how to pronounce it Um, and you basically have to give them all your information and they literally create a passport for you Uh, not a passport but a digital id for you guys Um, and then with the digital id you can k y c in any exchange basically as long as the k y c doesn't ask for an address As long as they're only asking for id you can k y c in any exchange if they ask for address You can't you can't you don't have no address. So you can't k y c within the address. Um So yeah, so that's what i'm currently doing if you don't want to go that route which I totally understand and and you probably shouldn't Um, then you can either use maxi or you can use bing x those are the two other exchanges that uh, that i've currently used in the us That uh, don't require any type of k y c. You only need a You only need what do you call it a vpn on? Timbers is a vpn safe what if by bit finds out so It happens it happens to me all the time where I You know either had my vpn off or I turned it off by mistake or I paused it so I can make a uber eats food delivery order um, and when and then I open up my app on bybit and it says Uh You know you're located in a country based on your ip you're located in a country that's not supported or not allowed And they basically log you out.   They forced you to they gave you 30 days to take all your funds out of your account and close your account so In a worst-case scenario, I imagine that's what bybit would do But again, like I said bybit has never done that um I've never seen it them do it. I've never heard of anyone Anyone's account getting closed. I've never heard of anyone losing money or anything like that on bybit Due to anything like that. So I think you're safe But the issue with bybit is that you can't you can't use it with only a vpn You have to kyc All right, so we've we've continued to get this bounce You can see we went up as high as 66 And I'm glad that I did not take along because price has dropped way back down All right guys, so I I think I'm gonna wrap things up here We've been live for about an hour and a half The idea was to to go live until we hit a new all-time high and as I was setting up for for the live stream Uh, the all-time high got hit. So I wasn't even able to be live While we hit an all-time high unfortunately, but um, I think I'm gonna wrap things up guys I think I gave you guys a few ideas on what we could potentially expect here We can see the support levels here This is the Fibonacci level that I'm gonna be personally watching today And maybe the rest of this week Depending on how price reacts there you can see right now. It's holding up fairly well Um, so that that might be a good trade setup there 65 500 level So, uh, I'll be watching that closely also this level right here 64 500 So I'll be watching those two levels closely and the final level right here at 63 thousand dollars to see if those Hold up as support if they do that's a potential trade their potential scout To uh to do there also rivers by the way I don't know if you've seen but we have in A auto trader if you have I don't know if you have access to trade on buybit if you do um You can set up an account basically That trades for you. So, uh You can see here. This is this is my Uh trading bot basically I gave it a thousand dollars. You can see a thousand dollars here. Um And in two weeks I'm up 200 dollars So, you know, if you're looking to get it back into trading, but you're scared the maybe to do it yourself Um, you can you can join the discord and this is this is definitely Something that that right now is making money. I've been testing it for two weeks now We're up 20 percent in two weeks, you know, it's not always going to be 20 percent in two weeks 20 percent is is actually pretty a pretty ridiculous number But if we can average anywhere between anywhere around 10 per cent per month, like that's a crazy crazy number That's a crazy return on a monthly basis. So Um, yeah, I would I would say check that out man. Uh, I could I could give you a discount if you're interested um If you're interested if you're interested in joining so let me know You could message me either in the comments or uh on instagram or on twitter And I'll be happy to share share discount with you Yeah, if you're gonna need yeah, if you're in the u.s. You're gonna need a digital id. It's not a passport It's a digital id. Let me show you really quick so that you know The site and what it looks like So it's this site right here. It's called rns. Well, the site is rns.id And you can see it's this country here Paula id it's a digital residency program So, you know, it's for identity verification k y c um You could get 180 days stay per entry, etc, etc And basically the way it works is you basically buy this right you can apply now for 248 um And that's pretty much it and then you can see that there's a lot of featured digital residents Including some really really big names like tim draper uh, the the the, uh Vitalik buttern So I think tim draper is let me see Founding digital resident So is he the founder i'm not even sure Maybe um, but we see ethereum co-founder minted voyager pass 1430 Yeah, so so it looks like he has one And uh, honestly, let me see I've never had any issues with it never heard of any issues with it Is it completely legal? I don't know, you know, maybe that's something that you can look into Uh, but it's it's an option if if you if you're looking to get on bybit or k y c This is the route that you'd have to take other than that you wouldn't be able to use it Right now for the bot it only this bot is only supported by KYC exchanges unfortunately, so So yeah, you would definitely need uh access to to one of those websites for now But uh, yeah, you can check it out All right guys, I am going we've been alive for about an hour and a half bitcoin already hit all time highs and dropped Uh down to 65 000. So uh, we're gonna keep watching here, but uh, I'm tuning out for now As you guys know if you guys want to follow me on instagram bitcoin.daily on twitter bitcoin xdaily On here you guys are already following me following me on here Hopefully make sure to subscribe if you're not turn on notifications We have a big video coming out this week. So make sure to tune in for that Or i'm gonna show you a cheat code that I have found to trade and make money passively in crypto and you don't have to Farm your crypto. You don't have to get into any high yield scams. You don't even have to trade it So make sure to tune in for that make sure to turn on notifications for that And uh, yeah, if you guys want to trade with me my link is in the description for the discord group guys Um Like I said, we have right now, you know, you could either subscribe to my personal day-to-day Scouts scalp trading you can subscribe to Uh, the algo signals that's giving you guys, you know about 100 signals per month You can even connect that to a bot that makes all the trades for you Or you can uh, subscribe to the options signals that we have a 100% win rate in 2024 Making crazy returns. So if you guys are interested link is in the description and that peace and love. See you guys


Hello friends, I am Sanjay Gupta. In this video, I am going to demonstrate you how you can calculate length of a string using recursion in C. Before starting, you can subscribe my YouTube channel by clicking on the link which is available at the bottom right corner of this video. You can download my app Techimage that is available on Google Play. You can connect with me by following these details which are available in front of you. Now I am going to implement the code for you which will count length of string using recursion in C. First of all, I am including a header file that is STDIO.H. Then I am declaring count function. This statement is function declaration. Name of function is count. It will receive an argument of pointer type. So I will be passing base address of the string. That's why I have mentioned character pointer and written type of this function is integer. Now I am defining main function here integer variable C and character array str is available. Now I am creating a printer function which will ask a string from user. With the help of getters function, I am going to read the values from the user inside str string. Now I am calling count function and passing str into it. This statement is known as function call. So count function is called str is passed as an argument. It will pass base address and the result will be stored inside C variable. Now printf statement will display length of string and at last return 0 because written type of main is integer. Now I have to implement definition of this count function. This block is known as function definition and this function will work as recursive function because I will be calling count function inside its definition. So first I am declaring a static variable whose initial value is 0. A static variable are those variables which are not initialized again and again. They use a previous value of a function in their next function call. So after static variable declaration I am implementing a base condition which is if asterisk str equals to null then it will return value of C else C will be incremented and return statement will call count function and inside count I am passing plus plus str. So plus plus str will increase the base address and next character will be checked. So this if condition is base condition. If it is true then recursive process will be terminated. If it is false then counter value will be incremented and this count function will be called. So this calling is recursive function call. This function call will call this function definition count and this process will repeat. If a base condition is true then it will be terminated otherwise counter variable will be incremented. So this is complete implementation which can count the total number of characters which are available in a string or you can say it can find find out length of the string. Now I am executing this code. It is asking for a string. So I am entering my name Sanjay you can see it is printing length of string that is 6 and also remember that here a total size of str is 10. So if you want to enter more than 10 characters then you have to increase this size because this is an static array. So if you want to read the size from the user you can convert it into dynamic array using malloc or calloc functions. So I hope you have understood how we can find out length of a string using recursion in C. Implement this code at your own so that you can understand this concept. If you want to watch more programming related videos you can subscribe my youtube channel that is sanjay gupta underscore tech school. Thank you for watching this video.