Okay, thank you very much for waking up early in the morning and be on time and I'd like to thank the organizers for this fabulous workshop, which I learned a lot and also for the very impressive and exciting environment that you created here in this workshop. So today I want to talk about two somewhat different topics, just mix them together, I mean to put them together. One is about broadly called the Newton's constant and the other one is about the symmetries all associated with localization and disclaimer, I will not talk about anything about the Wilson loop though. It's just a, you know, straightforward corollary from what I'm going to talk about. So this is all about my ongoing project. So this is not published yet. And so I think it's very ideal to discuss with the people and exchange the the idea and also get the comments from the expertise audience. The first issue is about the very old subject, which is large and scaling behavior of free energies and entropy and the known super conform theory theories and its avatar. Second one is issue which I think many people here expressed an interest in in this workshop, which is about the conserved and anomalous symmetries, all related in the context of a supersymmetric localization computation of some d-dimensional super conformal field theory. Schematically, that object I'm discussing here is this partition function and of course, it also means that they are all the co-relators, which is derived from this generating functional. And the first issue is about the dependence on n and also some coupling constant, g-square, which is generic expansion primary in the theory. And the second issue is associated with this functional integral measure. So let me start with the first topic, this large scaling of the free energy. If you are tabulated all known super conformal field theories and it's free energy scaling behavior respect to a large n, then you will notice that they have this regularity, namely it scales with non-universal dimension dependent order of one constant times n to the d over 2. For d called 3, 4, 5, 6 that we all know, it falls into this category. It's a very simple form and this clearly cries out for the explanations why it has a very simple form like this one. And of course, there's some caveat for computation of this scaling behavior and that we have to keep in mind. And we want to anyway, but we want to understand what this relation, how this relation comes about and what is the implication of this scaling behavior. By the way, I will not cite any, sorry, so I will not cite any papers here. It's just my habit and please arrest, be assured that your important original works are all well received and Okay, so yeah, now a question. Massive theory. No, I'm not, yeah, so that's the one important caveat. I'm not going to talk about here. The simple one. Yeah, that's different behavior. That's right. Yeah, okay. Yeah, I will not touch upon it. Yeah, that's because it's some of the normals from what I'm going to talk about. Thank you. So, you know, so let's just recall what ADS-CFD is after so many years. So in nutshell, the ADS-CFD correspondence states duality relation between some physical observables you compute in some ADS-D plus one dimensional gravity and the conformal field theory in D dimension, which shares the same kinematics in the spacetime symmetries. Each theory contains two coupling constants. That's a very important caveat for ADS-CFD to work. At least we can compare the two side by computing two of the observables in the two ADS and the CFT side. Otherwise, there's only half, therefore, it only remains as a conjecture. And ADS-D plus one, we have a Newton's constant, of course. And the other one is ADS-Radius scale, which sets the characteristic momentum or angular momentum. In D dimension and conformal field theory, we have rank of the gauge group or symmetry group, which is N. The other one is just a fixed coupling constant, G square. And weak coupling, we expand this one up for fixed N. And that's our conventional textbook quantum field theory perturbation expansions. Sorry, I couldn't hear you. Oh, that's right. So that's not, okay. That's just M theory, but I'm going to mention. So the way we understand is in terms of string theory reduction to type IIa, right, the five dimensional theories. Otherwise, we cannot compute anything from the CFT side. That's all I just meant. Okay. So physical observables on each side are, they're therefore computed in a double series expansion of these two coupling constants, respectively in ADS and CFT. And we reduce, that's exactly my point here. So reduce an M theory configuration, which has only one coupling constant, to type IIa configuration so that we now have two coupling constants to play with. One is coupling gate, a string coupling constant. The other one is roughly alpha prime, or maybe some other coupling constant. And if you have a more, more expansion parameter, that's better. That's always the corner we look for and do systematic and analytic computations of the given theory. So in ADS D plus one, a schematically, a physical observable called curly A is computed in weak gravity and weak curvature double series expansion. It's just double series form like this one. So you just compute in ADS gravity. And CFT also, I compute some observable, which has the same quantum number and expand in one of, in the, in the double, of the top expansion, namely one of N square plan expansion, as well as top coupling, coupling constant expansion in this way. So each of them are double series expansion. And we compare these two. Now, important thing is that the M theory, again, as I said, they're emphasized because we have only one coupling constant in M theory, namely Newton's constant. We cannot really reliably compute the physical quantity and either in CFT side or in gravity side. So what we always do is either in, we go into a type two way configurations where you do have a two coupling expansion parameters. Like in ABJM, we have the obi-fold parameter K and the other one is string coupling constant or in a five-dimensional reduction of the 2,0 theories where you again have coupling constant and the large M. So ADS correspondence implies that the A and A tilde are two physical observables must be equal. So based on this, we test all the, the consequences and whether, see if they are mutually compatible with each other. This means that these two series expansion must be somehow related. And here we have Newton's constant, ADS radius, the other one is one of N square and top coupling lambda. So that means these two parameters, coupling parameters should be related to these two. Namely, there should be some functional relation of, for example, the gravity side coupling parameters with conformity theory parameters. So this is a very generic relation we anticipate. And what furthermore, the reason why this would work is that in, in, in conformity field theory, in the way that we understand the large N expansion, when we make this double C expansion like this one, so this is one of the N-scaled expansion for fixed lambda and that's of course asymptotic expansion. However, for given N in the display expansion, for given the order in AD, one of N-scaled, namely the handle whole number H, the top coupling expansion, the this expansion is a convergent with the finite radius convergence. Therefore, we can read some perturbation theory in lambda and then analytic continue from the weak coupling regime to the strong coupling regime. So that's why we got all the mileage is in ADS CFT. So that allows this cranking up this whatever expressions we have this observables in CFT side to the large lambda region and then we can relate these two. And so this is a very generic relations that we anticipate just a priori. Now, the prototypical example of ADS CFT is any couple super young mills and there the relation we know is this one. So this relation between ADS and CFT is given by this function called G and R, that's function relation, but very mysteriously this functional dependence is such that this Newton's constant is related to only N, one of N squared and it's independent lambda and the other one ADS radius is related only to the lambda but not N. In general, we would expect some mixed functions of these two variables, but this is very special. However, this we should really view as an exceptional one rather than being generic. So we'd like to ask what our generic behavior of this interpolating function between CFT and ADS or vice versa. Of course, this function has to be invertible, otherwise this ADS CFT equality would not work. Now, this has to the fact that this has very special exceptional form is tied to the fact that among all CFTs we know of, this the any couple super young mill is derived from type 2b string theory, all the others are coming from type 2a or some variant of it. So in general situation we would anticipate somewhat deviating from this one and we'd like to understand how. Let's look at ABJM which is the another one, another the ADS CFT relation where we do have microscopic ABJM theory dual to ADS 4, the supergravity. There it is interpolating function is indeed when lambda this top coupling which is set by John Simon level and the rank N ratio of the N over K when that one is very large, it has this behavior. Indeed, it is function, it is a leading order behavior, it's a function of all of N square and lambda. And the radius of ADS somewhat again analogous to the any couple super young mill, so scared of lambda. But anyway, so this is a better, this is more generic than any couple super young mill theory. And because of this behavior and lambda being N over K, for fix the K in particular and K equal 1, which we go to M-theorem gene, this one gives you a scaling of this interpolating function which goes like N to the minus 3 half and this is a Newton's constant therefore the entropy which is 1 over G Newton's constant scales like N to the 3 half. So this mixing between two coupling constant in CFT is quite crucial to get this anticipated behavior as derived from ADSI supergravity computation. Okay, so again in M-theory case, as I said, this K equal 1 is set to 1, K K set to 1 therefore there was only one coupling parameter N and we artificially divided into Newton's constant ADS radius. They are just interrelated and that's M-theory regime. Now let's talk a little bit more about that, the expansion and see what that the implication is. So here everyone knows by heart that what this ABJM localization result is, this in terms of eigenvalues to UN times UN, I just take only parity invariant one and so this again is double expansion in 1 over N square and here top coupling is set by N divided by K where K is the level of John Simons of each UN gauge group. And we know from this integral the saddle point arise as a master value configuration when these, sorry, this I just mixed the connotations. Namda is the same as phi. Phi, this what I would call this eigenvalue, eigenvalues are scaling like square root of N and this also the other one is sort of square root of N. And in fact this scaling behavior is not so strange even though this just comes out of just the grand computation of the saddle point of this only large N. Remember that in the free matrix Gaussian matrix model, the Wigner distribution mobility edge ranges for this eigenvalue between square root of top coupling constant and its positive value. So the edge of that is precisely like a square root of N when you fix G-square to some constant value. So there must be some generic behavior, generic reason why the eigenvalue scales like square root of N even though this is not the general rule. There are some always exceptions. For example as this massive case is that already alluded. Now the interpolating function, the free energy has been computed from this localization and this function f of lambda which summarizes this interpolating function. This is the free energy Gaussian n-square times f of lambda is given by this one extreme weak coupling or strong coupling regime. And let's look at the strong coupling regime where top coupling is very large. Then we have this indeed the proclaimed one of a scale to lambda behavior which eventually gives you in the M theory limit n to the 3 half behavior. So this is it. So this we identify from this one and from the thin air that the ADS4 action, your own share action for this configuration is pi divided by 2 Newton's constant. We infer Newton's constant is given by one of n-square times f of lambda not one of n-square as in ADS5 case. So this f of lambda it is interpolating function here is plays a very crucial role in understanding the M theory behavior of this one. Now we have to do a little more test. I mean this is very thin the leading behavior in semi-classical approximation with a classical ADS gravity the action and we'd like to do more. And in particular as I said ADS CFT is a comparison between observable to observable. We just compare the identity operator. There are infinitely many other gauging very physical observable so we'd like to check the equality between the two. Now gravity is universal meaning that it just attract every energy source of mass source in the universal manner. In other words there's a coupling constant g Newton for every energy source. Therefore in gravity side correlation function is set by uniquely by this Newton's constant whatever it is. All others are kinematical factors like the polarization the prefactors. So that's not really setting the coupling constant. So we'd like to check this Newton's constant being exactly this form and see whether other physical observables in particular their correlators obeys same relation. For example suppose I compute M point correlation functions on the ADS side or equally in CFT side gauging variable operator. Here I suppress all the tensorial indices and I simply separate the positions and then I normalize all this operator by the two point functions. Good so if I do compute this one being the gravity observable the endpoint function should behave universally as g Newton to the n minus two over two power times order of one the position dependent factors as well as a tensorial index dependent factor. So we'd like to check whether this comes out right not just comparing only identity operator. So to do this we just follow textbook of quantum field theory we just introduce source and the value of the specter source and then find the response of the system. Okay this we can do one more for example when these operators are some tensorial press like energy momentum tensor we can squash the the the base manifold which is s three from round s three to squashed s three that's not the only one but that's one available already you know many people compute this one nicely so we can just take advantage of the result and we then extract the response of the CFT three around the round three sphere and see whether we get indeed this form. So here it's just a caricature of the squash three sphere here just I just you know the emphasize that a is a parameter which characterized the squashing a zero is round three sphere and a is one is extreme squashed one and this is the metric and also as you see the when I squash this three sphere I have to also turn on background for the the R current. So if I do this one then many people here compute this as an original beautiful work and the large and limit the localization of the free energy shows a very interesting factorized behavior namely it is given by the squash of free energy is given by round the three sphere free energy times some factor which which captures all the information about squashing. There is no dependence or mixture of the squashing into the function expression of this free energy on round three sphere and this is quite important even though this looks very trivial and seemingly the very innocuous actually the fact is precisely what we need to get the desired expression of universal behavioral gravitational couplings. So let's do a little bit of computation I will just sketch very briefly this very elementary computation so like any quantum field theory if I just introduce some source like in this case a squashing of three sphere then I can expand that is small squashing limit as a set of local operator insertions around round three sphere. I have just expanded here a a square a cube and associated with it there is an operator 010203 so on. In fact you can easily compute it by brute force that leading order leading order in A the operator precisely some linear combination of stress tensor as well as R current and this combination is quite reminiscent of some topological twist here. A second order you can expand this one now it's given by this O1 square and O2 however one point function in CF is always 0 therefore this two point function of O1 integer quantity is related to second derivative free energy respect to squashing parameter and lo and behold if I just look at this expression of this one and expanding powers of A I find that's just a number order of one times free energy of round three sphere. I can do the third order it's again given by the round three sphere free energy times order of one some coefficient and fourth order again is some linear combination of order of one coefficient and F0. What are these alphas they're coming in here that has to be the fact that here I have only one minimum coupling operator which is energy momentum tensor and R current and all other operator O2, O3 are different moment expansion of this operator with respect to angle among three sphere. So more generally sorry I missed the integral notation so here integer quantity by the way these are integer quantities because I'm taking here A to be the rigid value the constant number independent of the position on round three sphere. So the integrated two point function is given by the round three sphere free energy times order of one coefficient which depends on moment of moment expansion around three sphere which is the order of one integral and so this does not depend on n or lambda at all and then this one and we already know scales like n square F of lambda and likewise endpoint function is again order of one coefficient times n square F0 therefore n square F of lambda. Now the reason why all these different the moment the correlation functions scale like F of not and not in very differently is precisely because the innocuous of form that free energy is a factorized into round three sphere free energy times the squashing dependent factor otherwise it's all mixed up and different correlators will have different dependence and n and lambda and it's it will have a very complicated form. Now because it's a universal form if I compute endpoint correlation function normalized in two point function it will have this very universal form which we then read this as a Newton's constant expansion. What okay I'm okay so if that's the case I'm just re-deriving this from the localization. All right so all these operators as I said here the minimum coupling is only in term stress tensor and r column and all o n's are simply this energy momentum tensor then the weighted with furia mode of the three sphere or the spherical harmonics of three sphere and integrate over that's basically the the o n and therefore all these correlators are correlators t and j expanded in different moment. So these are in gravity side are nothing but the correlation functions of the graviton and gauge free or associated r current. So therefore this shows that the correlators of stress tensor are current universally controlled by Newton's constant and this given by this one scales as n to the minus 30 half. So this really completes not just comparison of the free energy but in terms of correlators that we have a Newton's constant coming out this way and this is the expansion parameter in m theory which goes like n to the minus 30 half. Okay so now we just illustrate this one in a specific example of ABJM. Now let's look at free energy of the dimensional CFT. Here I want to give some sort of heuristic maybe intuitive picture how we understand this the proclaimed behavior n to the d over two. Now all known CFTs that we define in the that we know of are defining some certain limit of d-brain world volume theory. In case of m theory m brain case we reduce in type 2a therefore you see certain suitable limit of the d-brain dynamics. So therefore the dynamical variables are the matrix value trivially. This implies that free energy of the mid-plan expansion one of n-scale expansion and there is an additional coupling constant which is top coupling parameter. So therefore that should play a certain role and here if I look at only fixed the top coupling coupling parameter and look at the large end behavior it goes like n to the d over two which I can decompose into this manner n square times the rest. Now n-scale the reason I pulled out n-scale is precisely like good old matrix model any matrix value the quantities should give free energy which scales like n-scale leading order. This is spherical topology of the warship. Now the other part is something we should explain. As I said this is for the I'm looking for the subset of those CFTs which has sort of maximum supersymmetries and then we can derive from the d-brain or m-brain dynamics. So the question is whether we can understand this extra this you know red colored extra factor which I will call anomalous factor and is there any simpler way of understanding the scaling. Now remember in ABJM example as well as you know Gaussian matrix model the mobility edge tells you that the the eigenvalue reaches up to order of square root of m and that I will use as the hint for the whole argument. Yes at least from localization we can explain does not mean that I understand the microscopic the dynamics or the nature of microstate in detail but just a number wise I can understand the scaling. Here I'll give only intuitive and heuristic argument rather than giving the details and in fact that the older the the core of the physics has nothing to do with special functions or the exact expressions of localization computation it's just only the physics. Recall that localization organizes computational partition function into classical part and one loop part and the rest does nothing maybe there's an instant on here I will press or the instant on assume I will I will assume instant on does not contribute in the large and limit in all those dimensions. Now if the integration variable eigenvalues have order of one distribution then the free and scarce like as n square exactly like a usual Gaussian matrix model and reflecting precise the fact that this is a matrix variable has a matrix variable origin. So this is precise comes out when tough coupling is very small but that's not the regime that we compare with the ADS ADS part and there we have to really take the tough coupling very large now the anomalous part which might scale like n to the alpha which we heard many times in this school and workshop scaling of integration variable that should arise in the large tough coupling regime from one loop part of this localization computation nowhere else in the classical part there's now nothing like this okay so how does that come about now remember what is a one-loop integral like any any quantum field theory one loop is around critical point in this case a q-core model you call a critical point you just compute the one loop determinant that's trace law that's this computation now here the m is set by the eigenvalue typical average value eigenvalue which is nothing but the Coulomb branch the values of the the scalar field and so one is computing this quantity well of course we are talking about supersymmetric system so you have to take a super trace now by supersymmetry leading divergence but not diverging leading power in m simply cancels out super trace m to the d whatever power that or cancels out and the in the in a maximal supersymmetric case the the first non zero non trivial contribution after taking supersymmetric trace it goes like precisely m square to d minus four over two that's from the sum null of the super trace m to d uh 2d on the Coulomb branch this master set by as i said this eigenvalue or scalar field value and this you know we always in the free pre potential we have the dimension of phi set to be the engineering dimension one so therefore we have this kind of relation in any dimension irrespective of the cft dimension now there from this one if phi is distributed by square root of n characteristic average value then we simply find that this one is precisely n to a d minus four over two i'm sorry which is precisely this value okay so this one is a leading power just coming from the trace and the top to the scaling and that comes out and the rest is precisely computed by the fact that phi is not order of one but scales like some order of square root of n the distribution in the eigenvalue distribution that's why this n to the d minus four over two is coming out okay well there is this is not always correct and there's a lower supersymmetric case i still don't have this universal behavior or something else i cannot make any universal i can extract any universal pattern but at least in maximum supersymmetric case this is this seems to precise the case and again again as i say that you know special functions we only need the asymptotics of the special functions the one of determinant and here all i allude to is a simple physics that is a boson fermion cancellation leading behavior which is not set to zero by supersymmetry has precise this behavior of this one okay now warning again localization is a way of computing number it does not tell you the microscopic dynamic there's no reason why eigenvalue should be weakly interacting effective degrees of freedom describing whatever n to the d over two entropies so i have nothing to say about it in fact i even suspect that using localization and trying to guess what the microstates are would be totally misleading so like i said so this is only for the maximum supersymmetric case extension to lower supersymmetries is you know still open and well okay good so i suppressed many steps here but this order of scale to the end in it's a winner distribution that comes out any couple super young male as you know very well in the wilson novel so the case and also the a b j m and the five-dimensional case that's always universal pattern okay so if i know if you ask me did i prove that this one is following from director of supersymmetry no probably okay i shouldn't say that i just inferred from the pattern of maximum supersymmetric case that this is uh the universal behavior independent of space time dimension so maybe i should ask if anyone has question at this i don't as i said i know that that's a very good question but i don't have any direct way of comparing this sort of reasoning to the m2m5 picture because i you know i don't know what the there's no direct relation so okay so what i'm alluding to is that the fact that we know that the five-dimensional super young male in the u v flows into the two comma zero that conjecture which i'm i'm tested assuming that okay so all what i'm based on is basically five-dimensional super young male theory argument actually i think that's because the cumulon is here i think it's uh you know uh just tangentially a question i always had is that when you have a two comma zero theory okay not the leader string theory and rank n then when you are in a cool tensor branch they have all these tenson i mean tension full m2 brain right like n or w bosons now if i bring them into the the center of the the tensor branch you know the critical i mean the conformal point then all these tension full string becomes tensionless there are infinitely many degrees of freedom at that point okay even even though we don't know how to count and how to you know explain or the describe the dynamics but it is the fact or at least we anticipate infinitely many degrees of freedom coming down compared to a coincident d-brains on the other hand d3 brain well there okay um but here is even more right six again haggled on like behavior that that's right so in that case you know d3 brain case is a composite one here it you think the higher massive string stays composite okay that's one way but otherwise i just want to bring up the puzzle that if you have infinitely string degrees of freedom coming down massless then you would say that there are infinitely many degrees field degrees of freedom at the conformal point on the other hand if i go to ads7 compute the free energy then it goes like n to the q so there's a no trace whatsoever of the tensionless string degrees of freedom there okay so maybe as as cumulon say one should view that those string states as composite unlike a fundamental string and it would be very interesting to check that carefully the next symmetries let's go back again to quantum field theory 101 unlike classical field theory quantum field theory requires not just writing down Lagrangian that's classical physics quantum fields require specification not only up operators in canonical of quantization formalism but also the choice of the vacuum without choice the vacuum it's like solving differential equation without boundary condition and or in path integral terminology quantum field theory requires specification of not only the action but also the integration measure integration measure is very important once you specify this one then you are completely spaced by the problem at quantum level and you can proceed to compute all the physical observables so here for example the generating functional in the with the source j you just compute the vacuum to vacuum transition amplitude in the presence of that source in the Lagrangian path integral okay so that clearly tells you that you have to specify what the vacuum is the second in pathogram terminology you are computing this one where phi is now classical field and now how on the other hand you have to specify what the measure is now in all the supersymmetric localization which is the local way of computing partition function and physical observables in supersymmetric conform field theory imagine that we do this one it's a path integral or maybe operator formulations where did we specify functional integral measure is there any option it's this unique and can it relate one if there are many prescription you can do can it relate one prescription path integral measure to another one and if so how so these are the questions we never as far as I remember we will never encounter this kind of discussions in the literature and here I'm bringing up the question I would illustrate the importance this point in operator formulation in a very simple example just to illustrate what the physics is and relegating path integral formulation and supersymmetric localization you know that's all you know sense just the details and the physics is not the more different and in my forthcoming paper the theory for illustration is a supersymmetric 2d free field theory and free field theory is the limit extreme limit of localization computation in other words you're doing how the computation and set the coupling constant to zero but you can just view it as just you know the standalone theory and supersymmetric 2d quantum field theory which is a free and this is of course you can view this as a string worksheet of the super strings and also it has a direct implication in in entanglement super some entanglement entropy computations that's how I come about this problem I will then show that two different choices of the vacuum of this free theory leads to two or equivalent two different choices of path integral measure leads to totally different theory totally different spectrum operator spectrum if I interpret this two-dimensional free field theory super some free field theory as the world should of nsr super string in string interpretation one choice of the world should vacuum leads to usual string theory of infinity tower started from massless and to all massive infinity tower the other one if I choose the other vacuum then it leads to the type two super gravity only there's no massive tower just super gravity okay this is bizarre but I just want to illustrate this one not because there's much to do with the localization because so trivial in localization technology but just to emphasize the vacuum choice is so dramatic let's illustrate first the simple physics that you know very well it consider two-dimensional fermions likewise any even dimension it's the same and it in two-dimension the fermions are the two separate conserved columns one is holomorphic j and the other entanglement j bar equivalently I guess recombine them into a diagonal vector and the axial orthogonal axial current now I can I decide to gauge this global symmetries and one way of the gauging it is just coupling minimally coupling this vector current to the vector potential a and that's the conventional QED two-dimensional baby version or four-dimensional QED and then in that case we know from textbook that the the axial j which was classical symmetry becomes anomalous in the background of this uh the the vector gauge field on the other end there's another one another choice you can do you can gauge axial u1 by coupling to the vector potential a and a bar then this one has to be conserved because you're coupling to the gauge potential on the other hand in that case a vector current total fermion number becomes anomalous and this is the familiar the baby version two-dimensional baby version of our wall this is something on the totally unfamiliar and of course standard model which is a chiral gauge theory is some linear combination in which we gauge this one and the the entanglement one in a different gauge symmetries the classical symmetry of two theories are exactly the same in these two conventional QED and axial QED you wouldn't distinguish them by just simply staring at classical Lagrangian classical occasional motion yet if you quantize the system in this manner then they will be completely different because they preserve different symmetries and make the the orthogonal other the alternate symmetries are anomalous so they are very very different okay now let's do the gravity now let's think about the you know as i as i alluded the two-dimensional free field theory as the warship theory of some super stream in that case we just use uh usual polar-capacitive integral formulation of the string theory and then we have it basically 2d super conformal matter and the coupled to uh 2d gravity or super gravity now the matter sector has two separate conserved column one is diffeuomorphism the other one is a biosymmetry these are classical column that are conserved at the quantum level what we can casually do is we preserve diffeuomorphism sensible and we uh sacrifice biosymmetry of course once we quantize coupled to 2d gravity and then there will be gravity compensating precise this uh vial anomalies but at the level of the meta-cft this vial column becomes anomalous okay i can choose alternative quantization which i will allude now which is that i gauge this vial column in other words i take this vial column as non-anomalous and conserved while sacrificing diffeuomorphism well it's not completely sacrificing it because i'm trading one degrees of freedom from one to the another it turns out that even though diffeuomorphism becomes anomalous it's not all the diffeuomorphism but only the area changing diffeuomorphism which becomes anomalous and there's a still on the area preserving on diffeuomorphism as the intact symmetry in the system again in this system like this q ed example classical symmetries of two systems exactly the same yet quantum symmetries are very distinct what are the consequences for the spectrum of the theory okay so i will just mention uh i'll just go through this one okay let's just recall very again very elementary uh chapter two in polchinski and i just consider this the bosonic part first of the supersymmetric free field theory in two dimension and i just just mode expand and then this is just usual the mode expansion of the holomorphic and holomorphic part of the the the free field and in canonical quantization okay these are operators now as i said we have to choose the vacuum to completely specify the theory i will choose the vacuum in such a way which is very standard namely it has zero momentum that's trivial central mass momentum is zero and an old annihilation operator in this heisenberg algebra analysis that vacuum okay in other words the vacuum is nothing but an element of a corner of this uh central mass momentum operator as well as a and a bar annihilation operators in this case the dual vacuum the sitting in the dual fox space is in one-to-one correspondence with the vacuum in the fox space however there's one caveat this is only if and only if the vacuum state is the zero is normalizable if it is not then there's an issue now let's choose different quantization now i will this is the conventional wheel everybody knows i will now pick up different one so in the same operator relation now i choose the the vacuum in such a way that for this right moving sector is exactly same as conventional one left moving one i choose the vacuum condition not to the ket state but the dual foc space brass state so these it has zero momentum with respect to brass state as well as the annihilation operators act on brass a vacuum is zero now you would say well this i can always relate to the uh originally the fox space relation by taking uh conjugate however if the vacuum is not normalizable then this is distinct from just the it's a the ket state statement and this uh non-normalizable state arises in many contexts simply the canonical example is Bose-Einstein condensate or in the quantum mechanics we encounter this kind of thing in rigged Hilbert space it's all non-normalizable mode it's background if i do this one then operator relation is exactly same with a with a simple composition one can show that actually the the two-point correlation function free boson actually takes a different form it's actually this one instead of z z uh z times z bar is a z or divide by z bar and this one as you can see preserve different symmetry from the conventional vacuum choice why the load and suppose the corresponds to z and z bar uh the uh scaling as gamma or gamma inverse this you can see its boundaries it's a gamma factor numerator gamma inverse in denominator so it goes like gamma square with respect to conformal transformation z and z bar scales the same way and here it cancel with each other remember in the usual case this is log z times log z bar at the plus log z bar in that case the with respect to conformal transformation z and z bar scales same way therefore becomes uh the anomalous whereas rodent's boost cancels off with each other so clearly even from this two-point function alone you can see that this choice of vacuum will preserve completely opposite symmetry complementary symmetry compared to standard quantization so here biosymmetry is respected whereas the different morphisms now you can just go uh the the counter quantization by looking at the uh the constraint of the verisoral algebra so here's the l0 and l0 bar and then here operator and then this side is as usual conventional vacuum this alternative vacuum where I choose the bra vacuum condition then this n bar is just you know passive integer that's the because this one is acting on the bra rather than the k now at the zero mode of this verisoral the constraint we have level matching condition as well as a mass share condition and it turns out that the the usual the uh the conventional vacuum choice of the the supersymmetric string the mass share condition acquires like the uh some anomalous uh the the cashmere energies and that sets the the uh the the intercept of the string excitation whereas the level matching condition simply says n and n bar equal the total of the oscillator number however here is the opposite here you have left moving the conventional vacuum and the right moving the alternative vacuum have opposite zero intercept number such that in mass share condition there is no anomalous factor here and only level matching condition that it appears and of course there's other higher verisoral moment uh to be satisfied so now we have basically n plus n bar is as number two and n minus n bar equal zero okay now if you look at the spectrum which satisfy that condition you find that in the let's say I here I also include the bosonic case but the first line is for the supersymmetric string with the GS projection if I have oscillate number one left moving an alternate vacuum choice number one one plus one equal two and that gives precisely massless super variety multiplied in nsns sector in the bosonic case for the curiosity if I just look at the further state then there are possible states namely n equal to n by equal zero or vice versa and they are nothing but just tachyon and it's a counterpart in the in this alternate vacuum so it just has the you know the cut two pairs of the tachyons so in supersymmetric case the only one which is allowed by this level matching condition is the the massless mode obviously which is the super gravity so in caricature the spectrum conventional string I have a left to moving a world oscillator state including zero mode and right moving state like that and level matching condition is left to moving minus right moving oscillator total number has to be zero so level by level there is always pair so we have infinitely many possibilities these are string states in this case alternate vacuum I have vacuum starting from zero and oscillate number and in the alternate vacuum it goes negative direction because of this brass state condition and when I demand the level matching condition the left to moving and right moving oscillator is the same then only zero mode remains okay so I intentionally did it in the operator formulation or one can do this all in the path inter languages now in a quantum filter we know that by adding local counter terms one symmetry one or normalist part of the symmetry can be moved into alternative part now there are many varieties of this one many infinite possibilities and complete classification alter quantization in the case supersymmetric localization is it's still to be studied because it's a cute homology which constrained possible the local counter terms you can add so the question is does the localization method work for all possible alternate definition of quantum field theory because if someone gives me supersymmetric quantum field theory and I didn't know any localization I would proceed with the definition of the vacuum or equivalently the function integral measure now somebody asked me I repeat the same computation with localization maybe there's constraint and in that case there is a tension why only a particular subset of possible theories automate the localization method computation so that's all and thank you very much for attention questions


Let's start. Improvements to font handling and there might be people who say that's shenanigans. What's all about that? Thing is, we have a lot of tickets in our bug tracker about fonts. Many are things that do not work. Font doesn't show up or is just crumbled or whatever. And many others are enhancement requests. I try to collect everything here in the pack cloud. Green is enhancement, yellow to red with importance are issues. I'm trying to talk about the green stuff. Only the green things because you need to be an expert to understand the problem with fonts when there's an issue. I will talk about three larger areas how fonts could be improved. The first one is things about substitution. That means you get a document with some alien font like Helvetica and you have to replace it because it's not on your system. That's quite a typical thing and it is implemented like this. Today you get in the standard toolbar a drop-down and the font name is written in italic for this font that is being replaced. The tooltip says this font is substituted. It does not work in the character dialogue so it's only in this drop-down. You don't know what font is actually replaced by what and you cannot... Okay, you know what I mean. So what do we have to do? First thing is I'm trying to put all the request tickets that we have into user stories. I start with a persona, the target user. We have two personas, Benjamin and Eve. I don't want to go into detail in the user story to tell you what is the problem, what the user wants to achieve for what reason. So Benjamin as the standard user does not care at all about the font. It has to work and I would say it works somehow but it's not perfect but it works for Benjamin. Eve, she wants to see what the actual replacement is for the current selection where the cursor is. But she also wants to see in case the document has more than one font, what is over the whole document, what is replaced in the document. Two simple requests and it could be solved like this. First of all, if you open a document, you can show easily an info bar here, there is something that has been replaced. You can get a link on it where you can go further to some dialogue where you can manipulate it, come later to this point. Second one is the drop-down that we have today. The font list drop-down could easily show what font has been replaced by which one. It's not a big deal, I guess. And finally, the dialogue at the bottom, it's also not a big thing to show here what happened. I will later come to the point with the icon. The icon is here the indicator for something special. So if you open the font list and a font is replaced, you get this icon here, some kind of warning icon. It is a bit better than the italic font, it is not really obvious what italic means. An icon is a better indicator for kind of warning. It is a warning. So what else? Second part of the request was that if wants to get an overview for the full document. And this overview could be in the document properties, we have a font section there. And it could provide a list of all fonts there with a nice overview. Because actually you don't want to get the name of the font. Helvetica or Times New Roman is replaced by Nimbus Roman. I don't care about the font names, I want to see what the difference is. What does it mean to substitute the font? And this preview could overlay two example images and show just nicely the difference. I think you will guess what's behind it. Next one. It is a feature also requested here for us that Microsoft has. If you store the document, do you still want to use the substituted font? Or do you the original or do you want to use the substituted font? There is no mean today, Microsoft hasn't. And it is requested. The second one, the restriction is about that we do not need to spam the document with fonts. If we save fonts in the document, it should be limited to the used stuff only. It belongs a little bit to the question. And solution is that we adjust a checkbox below this list. Again in the document properties dialog. Of course, Eve also wants to manipulate it. If Eve does not like how Nimbus replaces times, she might want to try another font, some liberation or whatever. And this is not a big deal. It could be a drop-down list or whatever here. It is just another request. So far for substitution, we have published it some time ago, two years or so on the design block. It is nothing new. New is that we also have a large list of fonts and the selection is not so easy. One issue here, for example, is that you get the Deja Vu fonts splitted into all the special expressions. The sun's light, sun's condensed. It's all one font. So that's an issue or something that can be improved. An issue is it because on MacOS you don't get the special things. The actual requirement is that the long list needs to be structured a little bit better. It should be easy to find the fonts that you are looking for and you don't want to get bothered by all the variations. A proposal on the ticket is that it goes into a submenu. So you open the drop-down and in the submenu you get variations of light and condense and whatever it is. Another idea is to have two drop-downs next to each other. In the first one you select the font and in the next one you select the style of this font. The third one is to indent the styles a little bit. None of these are really nice but we have to find a solution for this problem. Maybe I have it later. Next thing is that you not only want to get bothered by the styles, you also want to just get a condensed list of fonts that is useful in the current situation. Do I have an example? Yes, an example is on my system installed P052. I don't know where it comes from. It's something which belongs to X if I remember correctly or whatever. I also do not care about Greek and Hebrew and Arab. I don't speak any Arab so I would like to hide all these fonts that I never use to get a small list where I can find it more quickly than today. It becomes even more relevant with the new Noto fonts. It adds a lot to the selection. What we need is something to probably filter the font list. Request have been made to find favorites. Maybe I want to use a large number of fonts for my design work but usually I write documents and when I write documents I just want to have five different fonts to choose from. So I want to favor write things. I want to select fonts that are used for my local system. Chinese people probably do not care about fonts that don't have any of these Unicode pointers in it. And what else? Use fonts in the document is also something that you want to move on a specific position. There are some possible solutions. It's nothing that is completely new. TextMaker and Scribbers has a way to hide fonts from the UI. Just don't use it. It is here, this checkbox. We could do it kind of similar way in our options dialog. It is just a table that lists all the fonts. And what you click is shown on the right side with an option to make it a favorite. It's a checkbox. It's the options part. And to disable the active thing, meaning if something is not active it is not shown in the drop-down list. I would also condense the styles. That is my solution. Condensing means here the variations of Deja Vu Sans with nine different styles is just collapsed into one style. And if you want to get more, I'm a little bit too far, you have to do it in a special dialog. What we want to achieve is a small list of fonts that is well sorted and that informs me about my own favorites. I want to easily and quickly find what I'm looking for and what is being replaced. That is again what I told you before, it's a warning sign here, it's a different icon. And way too small to read. The style variation as I said is accessible in the character dialog so I would make it easy. I would make this drop-down as easy as possible and if you want to go with Deja Vu Sans condense special number three you have to go in the character style dialog or you just enter it. Maybe that could work as well. Sort order should be kept. The favorites get a favorite indicator and icon. Non-active fonts should be hidden in the list and non-local fonts could be activated as non-active by default.  I've seen the ten minutes left. There's one, it was quite fast. There's one button here at fonts and that is a requirement which comes from the installation thing. Design team talks a lot about what is to replace and do we ship the liberation and the open sans and noto and whatever. Things change and I think we should not talk about these aspects. We should not deal with font management at all. It is up to the user but if the user wants to install a font we should make it very easy and it is at font. It is kind of get hot new stuff known from KDE. It clicks a button. You get a short dialog which lists extensions, in this case font extensions on our extension site or whatever and you get a quick access and ordered to install it onto your system. The clue here is that the addition of this extension, in this case addition of fonts, is placed where you work with the things and this tight connection between the program and the extension site, that's important. So this management is kind of my pet. Next tab here is I think it is clear that you should be able to manipulate the substitution table. That's the second tab here in this configuration dialog and it shows again what you, it does not add anything new. You have screen lonely and screen printer. It is possible today and it is some weird way to, there is a third option all three or I don't remember. It is nothing new except the preview of how it looks if you replace it. Of course you should be able to manipulate the replacement table. I believe, yeah. That's a picture from today on our bug tracker. I don't know the him on TF91130 and his proposal is to not have a drop down. I didn't find a better place for it. Just put it on to the end. It is a brand new proposal and not my proposal. Left column shows the used ones and his request is why do we need to have just one drop down, one small list has plenty of space on the UI and we can have more columns in a certain way sorted so that, yeah, I think it's clear with the ideas. Show more on the screen. To summarize, we need improvements on the font substitution, the info bar, the substitution table should be more easily accessible. The drop down could receive some, need some love in the preview is really nice to have. That's actually what the user want. We need means to hide and highlight fonts, hide unused highlight favorites should go into the option dialogue and the font selection drop downs. All these stuff has to be reworked kind of and the last thing, the font extension thing so that we can, that the user is not, that we do not need to ship fonts. That's all. Thank you. We install fonts in this, yeah, the rationale behind why to not install fonts is a question, challenge, yes? We install fonts in a certain way. Our user directory and the fonts that we install are not available on the system. So if you are in Linux and you use a packet manager, you have two different ways to install stuff. It's a problem to me. I don't like it. And the other part is we ship fonts ourselves and probably spam users with unwanted stuff and the user cannot get rid of it. Let's say you don't like the Google stuff and you don't like Noto. What do you have to do? It is not that easy to find the right place to delete the file. That's, I have to admit it's rather my personal idea. I want to have a smaller base system and easy ways to extend it. There's font config and there are some substitution rules already. I think all a lot substitution rules already. Yeah, that's how it works today. Font config is the first step. Second is that we have a fixed list of association between fonts. Yeah, of course. I think some of these substitutions cannot be overridden. How do you deal with that? You are the expert in that field. No, I don't understand why we shouldn't make it possible for the user to deal with the substitution table more easily. It's not easy to go into the configuration somewhere deep in your system. You have to know that font config exists. You have to know how it works. You have to find the right configuration. You have to edit these replacement tables and it affects all applications everywhere. It feels not really like what the user wants. He wants probably for one document the windows font replaced by some certain or in the other way. User should somehow have the chance to... Yeah. But I think you have to approach the... I would generate this list. Somehow there has to be a default list of substitutions. Somehow it has to be generated by default and the user is only able to overwrite the default and the generation is font config on Linux. I don't know how it works on Windows. But yes, there are a lot of questions around the topic.


For anyone listening who's just trying to build a habit around movement and a sustainable habit around movement, that's what we're all about, the Scope Society, and just really leaning into movement that feels joyful, feels like something you actually look forward to showing up to and wanting to transform how we look at working out. If anyone's out there listening who wants to check it out, they can. Drop that quote again. What was it? Commit to less so that you can show up more.


Catherine Princess of Wales has been missing for a little while and now she's showing up again. Greg wants to tell us about the video we're going to watch. This is her official statement produced by the BBC and she's telling us what is going on in her life, quite simply that. I wanted to take this opportunity to say thank you personally for all the wonderful messages of support and for your understanding whilst I've been recovering from surgery. It has been an incredibly tough couple of months for our entire family, but I've had a fantastic medical team who have taken great care of me for which I'm so grateful. In January I underwent major abdominal surgery in London and at the time it was thought that my condition was non-cancerous. The surgery was successful, however tests after the operation found cancer had been present. My medical team therefore advised that I should undergo a course of preventative chemotherapy and I'm now in the early stages of that treatment. This of course came as a huge shock and William and I have been doing everything we can to process and manage this privately for the sake of our young family. As you can imagine this has taken time. It has taken me time to recover from major surgery in order to start my treatment, but most importantly it has taken us time to explain everything to George, Charlotte and Louis in a way that's appropriate for them and to reassure them that I'm going to be okay. As I've said to them I am well and getting stronger every day by focusing on the things that will help me heal in my mind, body and spirits. Having William by my side is a great source of comfort and reassurance too, as is the love, support and kindness that has been shown by so many of you. It means so much trust both. We hope that you'll understand that as a family we now need some time, space and privacy while I complete my treatment. My work has always brought me a deep sense of joy and I look forward to being back when I'm able, but for now I must focus on making a full recovery. At this time I'm also thinking of all those whose lives have been affected by cancer. For everyone facing this disease in whatever form, please do not lose faith or hope. You are not alone. All right Mark what do you get? Yeah so this is important. It has been shot by the BBC. You can go and get the 4k footage if you want to look at it close up. Important because it isn't the palace that has produced this. It's the BBC. You think what you want of the BBC, but I guess because there was a lot of speculation, conspiracy theory around this, the palace decided to have an outside organisation. Of course if you want to go down that route, yes the BBC was once part of MI5 and MI6, so if you want to go down that route keep on going and have a have a enjoy yourselves. But essentially the idea is that this is a true footage and so it's high quality. For example you can see a fly that goes across the screen in order to be digitised that would be really quite hard. You can see the lens flare from the ring. That means that light has to shine off the ring and be dispersed by the lens in the camera. You can hear the jets flying into Heathrow airport in the background. Now this is shot in Windsor. You have the daffodils in the background. You have the blossoms so we know the season in the background is the right season, the daffodils. The Queen Mother's, one of the Queen Mother's favourite flowers. When I used to live at West, at the old place of Siegfrieds, the Queen Mother would drive down every Easter around about this time in order to watch and see those daffodils, incredible display of daffodils at Sassoon there. On a wooden bench so it's very much of the people, the daffodil being the symbol of Marie Curie and the Cancer Foundation. So a Breton shirt being worn as well, a shirt of the people, for sailors. So the sailors, you could see them when they're drowning more easily, apparently. But what we know it to be is indigo along with the jeans. So it's very utilitarian. It's very much, shall we say, the people's princess. They're emulating Diana, her mother, yes, mother-in-law, would have been known to be her mother-in-law, and wearing Diana's ring there. So look, lots of imagery in there about the family and about cancer and about resilience. We're there at around Easter time and the daffodils blooming, reborn in the spring. Now, what can we say about her? Oh, by the way, here's an interesting one. That ring, by the way, was given to Harry by his mother in her will, and he gave it to William in order to give to Kate as her wedding ring. So actually quite somewhat magnanimous there from Harry. Not something you'd expect, but good on him for doing that. Look, there is a baseline here of concern and worry, I would say. I'm sure everybody else will go into that. But the first big break from baseline for me is this downward look and a big breath in and a small vocal click as well around this, of course, came as a huge shock. I would say that's pretty congruent for a huge shock. I don't find that out of place. So I see her look for the emotion, contain the emotion, and deliver after that more emotion, contained emotion around the big shock. What follows after that is a lot of self soothing, especially around the thumbs. That's what I expect with honesty around this. And then a baseline break as well, a look down, thinking about those who have been affected themselves by cancer. And ultimately, I'll finish on this is the job of a royal family to take the president, which is to be a fairground mirror, albeit sometimes a wobbly one, but a mirror of all of us, which is all of us have known people who have maybe cancer, but other some kind of life threatening disease. And I guess this speech then becomes a chance for us to think about those people in our lives, not just Kate, but those in our lives and think about them. And so she finishes this speech with the idea of faith and hope. And you're not alone. So lots of symbolism in there, some real emotion, I would say, in the right places for anybody speculating looks absolutely real and and congruent to me. Greg, what are you going on this one? Yeah, I'll just take one thing. I'll be plenty for the rest of you because, Mark, what a beautiful job of tying in it is impossible to fake all of those things in the background and tying it in and having the fly cross all of that beautiful. But there's one place that is palpable in everything she does, all of that hand adapting everything else. It takes a new turn when she digs her nails into her arm and she says, I'll be okay at the same time she I blocks. That's uncertainty. Clearly, the rest of her message is pretty certain. That's the place I see some anxiety and that kind of thing. When people do that, it's a change from the rest of their adapters. And I think that one stands out to me the most. Scott, what do you got? All right. Yeah, I agree with you. And I'll talk about this more as an entire piece, instead of going through the little things and cutting things up. If we look at her from the beginning to the end, we see a lot of changes. If you listen to the very beginning of it, then you scooch back to the end and listen, you hear their voices a lot lower at the end. Obviously, it would be because as you go through these things, you know, you relax. So I'm like quite often on this show, you'll see me I'll start off. Yeah, what's going on that I'm like laid down here. I'll relax and stuff from scoofing around and talking to stuff. But in this one, she does a great job at remaining really or fairly still, but we do see that movement happen with us. And the biggest movement is in her shoulder as it comes down from the beginning to the end. And the difference is there. After that, there's not a whole lot of difference other than her voice. Now being a little bit lower, which would make us think maybe she's a little tired because she starts off all bubbly and toward the end, she is talking about things that are really serious. And if she gets more emotional about it, I'm sure that's what's that's causing all those things. So there's no surprise in where she begins and where she ends or the differences in those two things. Also, the AI stuff, I agree with the mark. There are a couple of little glitches in there that won't I think Chase is going to talk about in a minute. And but I don't think it's AI either. AI hasn't been able to, you've got the two different things. You've got people and they do the deep fakes. I don't think it's a deep fake at all.  Some are really good. And we could argue about this. But everything from the illustrators with those things to the way their mouths move, those things that they haven't perfected that yet. They haven't perfected the body language of AI yet. I'm doing a whole video of that over on my channel. I've been working on it for a while and I go into those things. So I've been paying it. So tell you that because I've been paying attention to those things and focusing on them. So I don't see any of that going on in here at all. Like I said, there's a couple of little glitches I think that Chase will talk about. But outside of that, I think that's her sitting there talking. And I'll agree. I'll agree with you guys. The most we're seeing movement-wise is in her hands, which is where most people adapt, uses adapters when there's something going on. And her blink rate does go up and it does go down. And we do see eye blocking. We see all these things that we're familiar with when someone is stressed.  And I don't think she, from what she said, she didn't expect it to show up. So I'm sure it was a shock to her. And she's trying to get through that plus all this stuff in the media. Everybody's saying, ah, she's not there.  So I'm sure that's part of the stress for as well, which has made this really important. So I think with all that on your mind, plus your health situation, that's what's going to make you act this way because she's, she's really batting down there. Their legs crossing and her hands together and all that ringing and squeezing and adapting with her hands. I think that's a pretty big deal for her. Chase, what do you got? Yeah, y'all covered quite a bit there. I think when William and Kate came onto the scene, I think a lot of people were excited to see people who were open and authentic, which is rare for Royals. And at least here in the U.S., the Royal Family is seen as these people who are kind of artificial a little bit kind of walled off in isolation. And then in the past year with all the news about just from what I've read and I'm no expert, like there was some faked photo thing, like an AI enhanced or AI faked photo. I think people might have been upset about everything seeing that. Keep in mind, I'm no expert on the Royal Family. I'm not an AI expert. I won't say something's AI or not because I'm not an expert. The issues that they're going through, I think I only want to look at this as a behavior profiler. And I'm not sure what to think of this. There's not a whole lot of emotion and it's designed to be an emotional reveal. And I get that it's a Royal Family publication made by them, obviously the BBC. And maybe some of you who know this stuff way better than we do can add what we're missing down below. We're all open to being wrong here. There's a lot of pacifying behaviors here, which means we're stressed out. We're trying to comfort ourselves. There's a lot of uncertainty in her body language. So it's not just grieving and sadness that we're seeing. It's a lot of things that suggest uncertainty. And somehow her left shoulder and her left eyebrow are permanently just locked in this upward position. They do not move. She has a few bumps with her left shoulder, but her left eyebrow is raised and stuck in position. I thought that was very unusual to see. And obviously sorry to hear about the diagnosis. We're obviously thrilled. There's hope and things are looking up and happening to her to keep her healthy for her and for those precious babies of hers. But something about this video felt way off and I will admit that I can't put my finger on it. I don't know what it is. That's all I got. All right. Well, there you have it. Those are our thoughts on what's going on with Kate. And let us know in the comments what you think is happening. And we'll see you next time.


It is the dawn of a new era. Ladies and gentlemen, welcome back to the channel. My name is Jack the Buster. I'm Shinobi. We have episodes 385 and 386 today of our one-piece watch. So we are starting what on Crunchyroll is called the Summit War Saga, which leads me to believe there are some crazy stuff that's going to go down during this one. If you missed it, we just finished up Thriller Bark in the last episode. And man, did I enjoy the heck out of that arc. It had some ups and downs, but overall just Brooke being in addition to the crew just fits perfectly. I think in terms of the dynamic. So I'm excited to see what adventure we go on with him to start off, especially considering we're kind of still getting our legs with a thousand sunny and Frankie being a part of the crew. We're gonna hop right into it. If you need the channel, drop us up and hit that big white bell and let's get started. Marie Joy. The whole, this thing, it says hold land. Is that a typo? I thought it's holy land. Oh, shoot. Garp. I'm such a sucker for like these scenes. Sengoku's goat. Dude, I was wondering if you would have to answer for this. Yeah, because now they've gotten away from Garp and Kuma. Hmm, and Luffy had nothing to do with it. Hmm. Why that goat always eating paper? Yeah, that's kind of true actually, but people are going to find out either way. I think it has to do something in the fact that Kuma knows who Dragon is and knows that Luffy's like him. Why let go eat in paper? Oh, I love Garp, bro. Like I said, I figured that Kuma would have to answer to that to some extent because now the fact that they got away from Kuma is like, it's like undeniable that he let them go. One million percent. It seems like he didn't even have an answer. What? Oh my gosh, they're fishing. I just feel like the beginning of every new arc starts with them fishing and Brooke is part of it now. He's got a net. He just fits perfectly.   Yeah, but Kokeromer made sure he needs some distraction at all times or he just loses it. I lind. Oh, fish. Plenty of food. Shoppers swinging his legs. They're running from something. I think it's like a swimming from something. Storms of Bruin. So they said their log is leading them to the Navy headquarters, though. When they're under the impression that it's towards Fishman Island. Serpent currents. I like how they're, they're fits. They're very relaxed fits. Bro, what? They're just like monsoon tornadoes. Quite a pickle. Literally the entirety of the ship is in danger. Very cool. Nah, Sonny is capable. I feel very con- Oh, I think I should feel confident about Sonny. Is Nor gonna cut the wave? I mean, to be fair, they did blow open the wave on the way to Ines' Lobby. Blew a hole in it. It does seem like it is alive. It's like directly targeting them. The ship's not listening. I mean, Frankie should have an answer. The ship's not listening to what they're saying. This is a good test for Sonny. I mean, we went straight from Ines' Lobby to Thrower Vark without much of- Oh, okay, Brooke. Wait. That is so clean, man. Without really much of a trial for Sonny, but now we're testing the elements. They kinda, they look like snakes. I think it's pretty cool. Sing more about the world. Oh, my. Ew, why does that look so cursed?   Oh, true. Wait, yeah. Why don't they just launch out? Follow. I'm gonna be honest. It's probably a good thing we don't got Mary anymore as much as I miss Mary. A song! No, true. True book. Actually, is he gonna sing them away? They're writing it now. Hey, Frank, you said this trip was ca- Oh, my God, Chopper! Oh, my gosh. Chopper actually just almost perished. My boy. Thank goodness Robin's got that quick thinking. Holy. Fishmen. It's gotta be some kind of island. Oh, no, just- Oh, shoot. So that's the direct halfway point. Wait, so is past the red line the New World? The day they said they would make it. Oh, back when it was just five. Holy. Iconic. What is the mystery mountain? Guess what makes it the red line? Like, they mentioned it like one time, I think. The biggest one yet! It kind of looks like the upstream that sent him to Skypia. Yeah, I'm kind of proud of Sanji for manning the ship. Wow, look how ahead of the mark I was. Chopper and Usopp are so consistently just terrified, mortified. Just use it to your advantage, baby. There's so many people like man different things and situations like this now. Like, Brooke, one person makes such a big difference. Oh, they're out of there. Easy-peasy. I guess that was just like another trial. Wasn't even that like- I guess the sea inherently was attacking them, but that's just how the ground line is. It's so bright now. The red line. So is there like a similar way to cross it, like entering the ground line? Yeah, dude, 385 episodes? Okay, yeah, so it goes all the way around, so they actually have reached halfway, I see. If they went all the way along the red line, they would find Labun. I'm glad they did that diagram. That makes a lot more sense. They're all old five years ago with Croc. So she ended up with Croc after she got to the ground line, I think. She was with them like, what, three years? It's kind of a really big moment, actually. I mean, I didn't think they would make it a halfway point this quickly, but by the way they describe the New World, it's like they've climbed one tiny mountain in comparison to what's ahead. Oh, so they know how close they are to Navy HQ, I see. That's why they said it was leading them there. But inherently it's pointing to Fishman Island. Oh, this pool, that is so cute. That's such a good idea.  I'm surprised the world didn't end up with any permanent damage from the whole thing with Akuma. I guess mental permanent damage is a thing, though. Gotta be stronger. God dang! Holy. I feel like they never even showed him taking it completely all on because there's no way to even visualize what he took on, like the pain and whatnot, and what his reaction to it was. See, this little lookout is his sort of training room, that's cool. I guess it's the crow's nest. Does that transponder still have a straw hat on? Does that have a straw hat on? Classic. They're gonna have to get used to that. God dang it, Brooke. It's hard to defend you. Oh, shoot. They're in a submarine. That is so cool. So much application to everything that Sunny has to offer. They definitely went further than 5,000, then. None of you can swim! Do we hear the metal, like, tearing itself apart? Oh. Why does that look like a rabbit? They're so chill about this. She's like, I can't with them. They sent no responsible party aboard. Horror pairs. Aww. That's beautiful. Dead end. Oh, they're thinking about going, like, under? Oh, yeah, no. They point down. I feel like it's a good assumption that Fishman Island is, at least semi-underwater or semi-submerged if they're Fishmen. I feel like there's gonna be repairs needed for this submarine. Also, yeah, they just went down looking for it. Aww. Brooke's having so much fun. Oh, no, it's followed them. The sea rabbit. Just punch it, Luffy. He's gonna one-shot this creature. God, it even sounds weird. Since we've seen ours, it's all small in comparison. Oh, there's somebody inside. They can just save someone. Is it a mermaid? And a starfish? Oh, no. I'm saunty. Oh, my gosh. What is that? She got, like, a little clam backpack. She is a mermaid. Is this a starfish in his little hat, too? Are they not concerned that they just, like, landed on the ship? He's still has hard eyes, even unconscious. He's so easy, man. I mean, I feel like a mermaid would have a better idea. They probably found the perfect person to let them know where Fishman Island is. All right, well, an aptly confusing start to the arc, but it seems like we do have a lead to someone that, like I said, has a pretty good chance of knowing where Fishman Island would be. And reaching the red line is a big deal. That's a big moment. Episode 386, let's go. Saunty's just incapacitated, probably for a while, too. I honestly thought she was going to be scared of Brooke at first. Is she fine, just chilling on land? I guess Kokoro was. What a time. Free food! You're going to help by selling? Oh, my. She is, uh, interesting. Jewel of the sea! No, it's not! Kami? Yeah! It, like, killed his entire vibe. Oh, my gosh! It was Kokoro! Saunty is so subtle about everything. What?! Oh, he never found out? He called her a monster. Nami, it's just a natural instinct. Brooke, no! No, Brooke! She can't even be wearing bannies! Oh. He's asking for money? Fun, right? I love Brooke. Yeah, she's very easy to please. You bro. Bro, guys. Saunty doesn't want to know the answer to that question. Something's missing? What? He called it a little circle of fun. Glove! Do you have stitches? Papug. Is your pet Ann master? Oh, he's kind of cute! Papug. He has a song! Oh. Well, she feeds him? Well, she has, like, a clam backpack. Okay! Hey, Brooke, join in! I don't think that's that hard to clear up. Wow, that was just a song from the heart. Yay, thank you! Oh, ha ha ha! They are not paying any attention. Oh. He had a song from... Oh, look how sad he looks! I mistakenly thought I was a... What? He learned to speak on accident? A designer. Oh, man, I bet he could make some fire fits. You have to pay, apparently. Ashen. Blip, blip, blip, blip. Gah, gah! Oh, that's what... No, that's not why he said they were separated. He just said he was out of the circle of fun. That's villain music! Hachi. Why is that familiar? Hachi. Dopey macro? Look at Papug jumping around! The flying fish riders? What is going on at Fishman Island, bro? Rika little havoc. The lips changing are so... It's such a good detail. Octopus. Wait! No! Is that the hot shot from... From Arlong? Octopus, his name was Hachi.  No way. No way. God, thank Luffy, man. Oh, my gosh, it is. Flash to it. Really say that he was... I need to go back. I was still fixated on that being who I thought it was. Yeah, I was gonna say they can get really good information out. And these guys on the phone sound pretty goofy.  They said they would usually lose the hot shot. What was the attack, Koyaki? That's a big deal! Well, now it matters! Takoyaki! We got a map. Grove 44. Archipelago. Lionfish Ratter. Baudi. It had two dots over, though. Would it be sub-Baudi? Archipelago? Archipelago? I know how to speak. Is she calling fish? She is! They can help fight. A fish army. Oh, they look so cute. Kind of derpy, but cute. Oh, she can actually just command them. That's cool. Flying fish riders. That sounds kind of cool. It sounds like, like, from Avatar. I don't think she'd be okay without, like, asking them to sacrifice themselves. Dang, dude, maybe we need a mermaid as part of the crew.  That's very convenient. That is insanely convenient. Especially on the grand line where directions don't make sense. Hey, Kami, you looking for a line of work? Why does he hit her so hard? The next lead awaits. The lead to the, lead to the Fishman Island. Oh, yeah, I forgot what got one. This is cute, too. Oh, is this the flying Fishman? Oh, man. It's kind of a cool base. Wait, this is a really cool base. Oh, my gosh. Master Duvall. No, yeah, there he is! That is Hot Sean! Oh, my God. He's huge. Never mind. It kind of sounded like a push over. Valuable merchandise. Kami? You guys on the left's hair is something else. Oh, my gosh. I cannot believe it's Hot Sean. God, dang, dude. He was probably the nicest one out of all of Arlong's men. Oh, they actually fly fish, I see. Are they, like, bombers? God, dang, dude, Arlong ever makes a return as me nuts. I feel like there could be a lot of connections to him at Fishman Island, too. And Hot Sean is proof of that. Oh, God, would have Kokoro in their memory. Human trade is a booming business in Saabadi archipelago? Yeah, for real. What? Oh. That's why they said she was, like, a merchandise. He was very kind, yeah. He kind of just seemed a letter stray. Yeah. Guys, come on. Let bygones be bygones. Well, I feel like they're going to be nothing. Like, they're going to be so easy to beat. And Duvall looks like an absolute unit, too. Searching for someone. That's got to be some lore stuff. Nobody knows what he looks like behind the mask, and he's searching for someone. She said Luffy Chin. Is that an honorific? Yo-ho-ho. God, dude, having a musician makes everything so much better. Ha-ha-ha-ha-ha. Chopper finally has someone his own size. This feels so positive right now after how dark Thriller Bark was and how doom and gloom the entire thing with Kuma was. Even the Fisher Hype. Oh, oh, they've arrived. The flying boys. They apologize. All right, anti-aircraft. Just shoot them down. Are they that high in the air that you can't see them? She's hopping. Oh, my gosh. They're coming straight for the ship. They are like dive bombers. It doesn't seem like they have a ton of artillery, though. This is so absurd. I love it. They look like motorcycles. They're built like them. Contact the boss. I mean, yeah, they have a big name for themselves. I feel like Luffy could just straight up snipe them out of the air with his fist. They're coming down. Oh, my God, they're actually bombing them. And they have counterplay to it. I need Frankie to start like shooting at him with drawing. Duvall is a smart, smart leader. If he knows it's the straw hats and he's like, he just confirmed it and he's like, come back. He knows very smart. Those guys were done. So the next time they did a drive by looks like a horseshoe. Those are three macros and then this is Duvall. Oh my. Oh, that's who he's been waiting for. That's who he's been looking for. Oh, shoot.  Who in God's name is this? Okay. Well, I'm guessing we have met whoever Duvall is then. I'm trying to see. He has like a scar on the left here. I see his jaw. If that's Morgan, that's going to be absolutely insane. That's my only guess though. Morgan is the only guy that was this size and his jaw is also like I said, it's like metal. I don't think we've known anyone else that's been this size besides Arlong, but Arlong is a fish. I think you can tell by his skin. Either way, a very interesting lead, a very cool, I guess, sort of start to this whole saga and a cool tie back to Hatch on being there. What a throwback. They were talking about nostalgia the episode before this and God dang nostalgia is right.  But again, yeah, he was the nicest one there. It seemed like the entire time he was kind of just let us stray sort of like a lot of Marines where they think they're fighting for good. But guys, that's been it for episodes 3, 5, 3, 6 or start the next saga of one piece. If you're new to the channel, drop a sub so you don't miss anything and I'll catch you in the next one. Peace.