a few minutes. I think it's one minute, so I'm going to wait a minute. The clock is in his computer. It's 10 minutes ahead. I don't know how he managed to do this. I don't know what he would have been saying. Now I start. All right, guys, welcome back. Now we have the last talk of the day, the last lecture, by Diego Tancanelli, who's going to continue to explain which moves and this biography. Just before Diego starts, one quick announcement, the session after this talk, the discussion session, will start right after Diego's talk, OK? So it won't be a break. So right after Diego's done, we will start the discussion, and then the way we finish the lecture, OK? So, Diego? OK, so I suspect the last few minutes of yesterday's lecture were too fast. So let me go over this giant Wilson-Lew business one more time and just repeat the main ideas. So the crucial thing is that, OK, so there is something that weighs order n square, which is the n equal to 4, Super Young-Mills, action, or equivalently the Wigner semicircle distribution, or equivalently the ADS-5 times S5 background, OK? So this is something which is fixed at this order in the n counting. And then, OK, we inserted something that goes like order, sorry, first let's go order one, which was the Wilson-Lew in the fundamental representation. And correspondingly, we had this trace e to the 2 pi m in the pat integral. And correspondingly, we had a fundamental string in the back, OK? So in particular, this fundamental string in the back, I haven't really emphasized this yesterday. I said it a couple of times, but maybe I should really emphasize this more that the induced metric of this object, if you compute it, is ADS-2, OK? So there is a surface, which is a minimal surface, which it has a disc topology. It ends on the circle, and it has ADS-2 metric, OK? But now, OK, we can ask, OK, what happens if we insert something heavier? And so the next thing that you can think of is something which scales like n. And in the gauge theory side would be with the loops with a representation, which is either a symmetric or anti-symmetric of SUn, where k is of order n. So we have either a row of k order n boxes for the symmetric representation, or we have a column with k order n boxes for the anti-symmetric representation, OK? So in the matrix model point of view, this was the topic in one of the exercises. And you can think of having just an isolated point outside the vigorous semicircle distribution or having a missing point in the distribution in case of a symmetric anti-symmetric representation, OK? But anyway, so there is, again, some other insertion of this matrix. And then in the background, we have either D3 or D5 brains. But the crucial point is that both of these things are probes. So both the string and the brains are probes that do not change the background geometry, OK? And OK, so how we understand that the D3 or D5 brain, or how do we understand, for example, this ADS2 factor from a symmetric point of view? Well, simply from the fact that what we have, so as an operator, there was some loop insertion. It's either a line or a circle. It's actually simpler to think about the line, although the result doesn't change if we consider a circle. It's just that the way the symmetries are realized is different. But let's think about the line. It's a line in R4 times one point on this S5 internal space, OK? So we have, as I told you yesterday, SL2R times SO3 coming from this part, SO3, times SO5 coming from this other part. So we have ADS2 times S2 times S4, OK? So again, this is just the remnant of the conformal group, which is left unbroken by adding a line, which has three generators. I can do three transformations along the line. I can translate along the line. I can do a dilatation along the line. And I can do a special conformal transformation along the line. So it's three generators, SL2R. Then around any point of the line, I've got a sphere, SO3. And then since I fix this coupling to a scale has to be 1, 0, 0, 0, 0, 0, I break the SO6, our symmetry, down to SO5, which explains this. And again, in terms of isometries of the background, I preserve this thing. And there are associated supersymmetries. Half of the supersymmetries of the background are preserved. And you can really write down even the supergroup, if you want, is this OSP 4 star 4. OK, so now the important point is focusing on these higher representations is that we have an extra parameter in the game, which is this k, the number of boxes in my young tableau. And so the natural question is, how do I see k holographically? So what does this become? And so if you think about it, what happens is that there's going to be some fluxes treading either VS2 or VS4, depending on which brain you consider. And this flux is going to be quantized and is going to tell you how many boxes you're putting in your representation. So this is the computation I've done the other day. So there is some, in the DBI action, there is some gauge field on the volume of the brain. And this gauge field, so I got pi mu nu, which is the conjugate momentum to this gauge field. And if you do the computation, if you compare how the brain couples to the B field and our string compares to the B field, you discover that the condition is this one. So you discover that A and B, if you want the VS2 directions. So the gauge field is turned on along the VS2 direction. And if you integrate the momentum on the sphere, so this will be VS2 in the case of a D3 brain, or it would be the S4 in the case of a D5 brain, you get precisely this information about the number of boxes in the representation. Good. OK, so now what we can do, we can actually do computations and we can check this from the, so we can check this idea, this derivation with the matrix model and localization. So let me start with the D3 brain. I'm not going to do the full computation because it would take me too long, but I'm going to give you the gist of the argument.  You've got a determinant mu nu g mu nu plus 2 pi over the square root of lambda f mu nu. So this is the DBI action. And then you have the sumino term, which is one of the four factorial, epsilon mu nu lambda rho c mu nu lambda rho. So this is the tension of a D3 brain. This is one of the tension of the fundamental string. And essentially what you want to do, you want to find the solution. And so we know what was the, and think about the circle because this is the one that we want to, I mean, which has a non-trivial expectation value that we can compare interesting to the matrix model. So if you want this was the minimal surface for the string, now you can think that what's going to happen is that I'm going to add a cycle, this S2, which is going to be at any point of this minimal surface. So it's like this sheet of the string, which is puffing up and it's becoming fat. So this is why these objects are called giant objects. And it pinches back to the boundary. So this becomes like, well, I cannot really draw in dimensions, but think that this would be something like this all around the circle. And it pinches off. So the cycle shrinks when you go to the boundary and you land again on the Woodson lobe. So how do you get the solution? Well, this is a more complicated problem than what we did for the string. But in the string, we learn a trick. So the way you do it, you first solve for the line, which is simple, and then you do an inversion, and you get the circular Woodson loop. So start with the line, and then you have a line along, let's call it the x direction. Then you have an AdS2 times S2 for volume. So this is along the x and z directions. Now, you don't get the same answer in the expectation value, because when you evaluate the action, indeed, you get either 1 or something on trivial. But if I want to find the solution, I can use this method, of course. And then I got some sphere with radius r of z, such that r at 0 is equal to 0, so the sphere shrinks. So you can do this computation. I've wrote down some more details. I mean, there's many, many. I cannot really do it in real time. But the important thing is that there is a C4, which has this form, dr times the volume of S2. And then you have the gauge field, which is 2 pi over square root of lambda fxz. And then, OK, so if you do the computation, you discover that there is a natural parameter, a natural combination of the parameters that appears, which is this kappa equal to square root of lambda k over 4n. So this is a parameter that controls your solution. OK, so you first find the straight line, the straight line is simple. Essentially, the solution of the straight line is this r equal to kappa times z. And this f is equal to i over z squared. So this is the solution for the line. It's very simple. So you see it's a line with a sphere with a radius that grows like this linearly in the bulk. Anyway, so after you have the solution, you do that inversion that I was discussing yesterday for the string. You get your solution for the circle. You plug it in. You have, again, to be careful about boundary terms. So you have to add these Legendre transforms. But after you do everything carefully, and so all the details are in this paper 05, 011, 09, you discover that the action of the d3 is going to be minus 2n kappa 1 plus kappa squared plus arc sinh of kappa. OK, so it is some result. And if you've done your exercise, you're going to find that this is precisely the answer from the matrix model in this representation. OK, in this, yes. Yes, the definition of SE4. In which gauge? In which gauge you take this? It's not really been sorted out. But OK, so you can couple with three form that acts like that. The circle that the gauge transformation is, what they find at the boundary, and that's what induces the harmony in the expectation boundaries? I don't know if it is right to the same thing. No, because if everything is taking variance, then the actual action of the line and the circle should be the same. All you did was do a coordinate transformation, right? We would not know if it would have been between the circle and the line. Even within the circle. Even within the circle, yeah. In one case, in one case or the other, you have to write the best middle term. Right. Yeah, so here is written in a sense respecting all the symmetries and the most natural choice that you can have, which is this essentially volume form. But yeah, so there could be some harmony. OK, so anyway, so the thing is that if you take now, so this is your result. So if you take kappa going to 0, so you find that the expectation value of the symmetric representation goes like k power, so the kth power of the result for a single fundamental string. So this would be the result for a fundamental string to the power k. And so the interpretation of this result is the following. So from the matrix model, you have this. So the trace of this insertion is one of the k factorial. So the trace e to pi m to the k. So this is the term with the largest number of traces plus the expectation value of some other term, which has k minus 1 traces. OK, so something which has less traces than this. OK, so this is essentially, as I was mentioning here, so this is the leading term in this limit is just adding k fundamental strings one on top of each other. But then when you go to higher kappa, which is higher k, so this is k this parameter that I can control, I start deviating from this situation in which I just have some coincident strings if you want. And so the terms with less traces are becoming important, and they start combining in an untrivial way. So and this interpretation is, sorry, if you write down, this is actually n to the k, k factorial, w the fundamental to the power k plus orders, and k minus 1 if you include all the normalization and you're careful about normalization. So this is, you start seeing how increasing k, you start including non-planar corrections, one over n corrections. OK, so you have this extra parameter k that allows you to explore these extra corrections. And so the statement is that this action knows about all the one over n corrections in this particular combination kappa and resum測m. OK, so the complete result is a resummation of lambda k squared over n to the n corrections. Good, so now I'm running a little bit late, so let me be fast for the defi brain. You do the same thing, actually. This is a simpler situation because you have an AdS2 times S4, where the AdS2 is AdS5, and the S4 is in the S5. OK, it's a simpler situation, and as I was mentioning yesterday, you see right now you have some polar angle on the S5, and this polar angle controls the location of the S4. So you can write d omega 5 as d theta squared plus sine square of theta d omega 4 squared, of course. So you have this angle theta, which is some polar angle. And now this angle theta is determined by this equation. So now you see that the important parameter that appears in the game is not this kappa, but it is this guy. It's just k over n. So there is no factor of square root of lambda. And you can understand this because in terms of just tension of d-brain, so the defi brain is heavier by a factor of square root of lambda than the d-t brain. So you have this particular combination, so k enters here. And so now you understand that theta cannot be larger than pi, and otherwise you don't have a solution. It's a polar angle. And so theta less than pi implies that k has to be less or equal than n, which is consistent for an anti-symmetric representation. You cannot have more boxes than n. But anyway, so if you compute the initial action, and again, you compare it with the matrix model, you find agreement. And again, you have a resumption of these powers. Finally, a very interesting situation. So let's. The spring chart by the definition that you gave. I mean, I guess you have to generalize it for the d-5, right? I did. So k is an integral of. Yeah, yeah, on the sphere, on the sp minus 4. So that's going to be an integral over the s-4. Yes. And that integral, the result of that integral is that condition there, or? Yeah, more or less. So this is, yeah, yeah, so. Right. And that integral is 0 for theta equal to 0. That's how you see that the charge, which you're saying is that the b-fibrin cannot have charge more than n. Yes, yes, yes. Precisely. So let's cement. So we had the fundamental representation. We had an f-1.  We have a d-3 brain. Then we go to the anti-symmetric representation. We have a d-5 brain. So you have this situation here, this situation here. But of course, now, and OK. So this was order 1 insertion. This was order n insertion. But then now it's natural to consider, OK, what happens if I got an order n-square insertion? So for example, if I take a large young tableau, which has order n on this side, order n on this other side. Of course, now, you don't have AdS-5 cross S5 anymore. Because these weights in the same way as the background. So there is a back reaction. And you create a different geometry. So these geometries are called bubbling geometries. And they are very nice. They are very, so I like them for various reasons. But let me tell you also what is the bubbling geometry. So first of all, this is a half-EPS geometry. Because it corresponds to a half-EPS operator. Asymptotically, AdS-5 crosses 5. But then when you go deep, well, when you go inside of AdS-5 times S5, it becomes something complicated. And however, it has to preserve the same symmetries of a loop. So I can do an ansatz, which is dS squared. So it has to contain AdS-2. It has to contain omega-2. It has to contain omega-4. OK, so now we have 2, 4, 8. Direction plus remaining 2 ones. And then I got some fiber over this base. So I got f1 squared, f2 squared, f4 squared, where this f1, f2, f4 are functions of sigma. So this sigma is the upper half plane. So how do you get this solution? Essentially, you have to use killing spinors. So there is a very nice, powerful formalism developed by Gauntlet and other people, and then used extensively by UCLA group, like Docker, Gottperle, and other people, as this, in which they computed lots of bubbling geometries for lots of different symmetry groups. And so I mean, there is an algorithm. It's a very complicated algorithm, but it's an algorithm. And anyway, so what you find is that, OK, you have this solution. And in order to have a regular solution, you have to impose boundary conditions on the boundary of sigma. And there are essentially binary boundary conditions. You can have either 0, 1, or 1-1-1-1 for some fields. And so you can essentially define intervals in this boundary of sigma. So for example, in this region in blue, you get that f4 goes to 0. The regions in white, you get that the f2 goes to 0. So now you can consider, for example, a sphere like the s4, vibrated over an interval connecting two blue regions. And this will give you ns5. You can consider the s2 vibrated along two regions in which the f2 goes to 0. You are going to give ns3. Anyway, so you have cycles popping up. And this is why it's called bubbling. It's like bubbles of spheres in this game. OK, and then you can solve everything. So the whole metric is encoded in an hyperalytic curve. So essentially, you give me a distribution of white and blue regions on this line. And I produce to you a half EPS solution which respects ads2 times s2 times s4 and preserves half of a supersymmetry. So now, of course, the question is, what is the relation between these blue regions and white regions and the Wilson loop that I'm sorting? And this is the picture that I tried to draw the other day in which you have this Wilson loop that you write down as a. So this would be the representation that you write in this oblique way. And then you project down these sides. OK, missing something. And then, OK, this would be like the blue regions or the other one is the blue regions. But anyway, there is a very precise mapping between. So on the matrix model, the point of view is would be a multi-matrix model with multi-cuts. And so you have very precise mapping between the spectra curve, the resolvent that appears in the matrix model with these particular cuts and the geometry with cuts given I mean with this boundary conditions given by those cuts. OK, so there is a very, very precise formula. And you can think of it as an example of emergent geometry. So you have an auxiliary structure, a matrix model, which has nothing to do with geometry. But it knows about some half EPS geometry with ADS 5 times S5 boundary conditions. Yeah, OK, I guess isn't it the same? Yeah, I think it is the same. So you have a big matrix M, but now you can divide it into blocks. And every block is non-diagonal, but after you. So every block gives rise to a different, I think it's called multi-matrix model or multi-cut. I think it's the same thing. Yes? Give me a tableau. Yeah, so I give you a tableau. I can compute the matrix model. And then I can compare it with the super gravity with a solution that has precisely the same structure of cuts. OK, good. So I think I'm more or less on time. So I want to do now more. So OK, again, I like this picture a lot because of this emergent geometry thing. So this is not just ADS 5 cross S5. This is a very complicated geometry. And all the information about this geometry is encoded in a resolvent of a matrix model. So this is interesting for me. Yes? If you use cases of decode. It would be the case in which you have only one cut. So it's like having just one, for example, just this line. And then you just project down this guy and you have only one. OK, so well, you don't have a bubbling geometry in the case. You don't have a back reaction on the geometry. So yeah, let me say, originally, so we had large edges of this giant tableau in order.   The interaction between these distributions, it's simpler. And this is what we compare to supergravity. But then from the matrix point of view, then Leo had a more recent paper in which they can solve this thing for generic edges. OK, so now I'm going to briefly review some other contours, some other operators which are all related to each other and can also be computed using localization. So this is going to be the extra. So time permitted. So I'm going to do the extra. So more examples. So and for this part, I'm following a nice review by Zarembo, which is in this big review on localization and there is a chapter on with all loops. But OK, I have to say that many of these things have actually been done by Diego Correa always sitting here. OK, so the first example that I'm going to consider is a wavy line. So this is no longer a supersymmetric operator because we know that the operators are either lines or circles unless they do something peculiar to the scalars. So now let's consider just a line. And then consider some waviness associated to this line. So let me parameterize this waviness. So I got the parameter s going along the thing. So I got x i of s that tells me how this wavy line differs from the straight line. So for example, something like this parameterization. So I got the line along the forward direction plus some waviness from some small deviation. And now I can consider the combined propagator. So remember, I'm going to write down the definition again. So this is delta AB GM. OK, so this is the combined propagator. Of course, it's no longer 0. But it has this expression. Of course, I can do much more if I don't tell you what x i is. But even so, at small lambda, I can compute, for example, for the fundamental representation, this thing. And it becomes 32 pi squared integral between minus infinity and infinity ds1, ds2, psi dot 1, psi dot 2 squared. OK, so at this point, I'm just doing this computation.  So if you do this computation in QED, you are going to find LaRmov's formula for the radiation, for the energy radiated by an electron. So I'm going to define this pre-factor as B over 2. And so this is a Bram-Strahlung function. Again, so if you compute it in QED, B would be equal to 2 alpha over 3 pi. So you have this LaRmov formula for the energy of radiated by an electron. OK, so this is something that we can consider. We can define. And this is the first example. Now I'm going to move to the second example and then the third and the fourth. And then we're going to see that we are all related to each other. So the second example is called CASP, Anomalous Dimension. So now I'm considering, so again, I'm in Euclidean signature. And I'm considering, so this would be a line. But at some point, I introduce a CASP.  So the line goes like this. So we know from quantum field theory that if you compute, so usually in quantum field theory, you have a linear divergence in the Winsor loop. But we saw that this linear divergence disappeared once you consider the gauge field plus the scalars together. But we know that if you consider a CASP contour or a self-intersecting contour, you get on top of the linear divergence, you get a log divergence. And the log divergence survives supersimid. I mean, survives the coupling to the scalars. So you're still going to get a linear log divergence. And so let's regularize it by introducing two cutoffs. So one is L, which is an infrared cutoff, and epsilon, which is a UV cutoff. So you can think of like, OK, L is the cutoff at which the CASP line starts deviating from being a straight line. And epsilon, you can think of smoothing out the angle, the sharp angle, at a distance epsilon. So this is some epsilon here and some L here. OK, so now I can compute the, so let me parameterize this loop using the letter S before I reach the CASP and the letter T after the CASP. So I can compute this at weak coupling, and I got 1 plus lambda over 8 pi squared, the integral between 0 and L dS dt, 1 minus cosine of phi, S squared plus d squared plus 2 Sd cosine of phi. So 1 plus lambda 8 pi squared phi, 1 minus cosine of phi, sine of phi. So this integral is going to give you a log divergence that is expected. And that actually contains interesting physical information. So now we define this to be equal to some constant over epsilon. So gamma CASP, which depends on lambda and phi. So in general, this will some loop. You can, with this CASP, we can write it down like this for any value of lambda. So at weak coupling, it would be this particular expression. In general, we introduce a function of lambda and phi. So we see in particular that at weak coupling, this gamma CASP becomes lambda over 8 pi squared phi tangent of phi over 2 plus orders lambda squared. So we just computed it. Yes? Which one? That's fine. Yeah, so this goes here. So now you can do an analytic continuation in which this phi becomes i theta, becomes an imaginary angle. And this is like going to a Minkowski contour with a kick. So you get a particle which stays at the origin and suddenly gets kicked, and it moves in a theta direction. So now gamma CASP lambda i theta, when theta goes to infinity, now you can take the limit of very large theta. And this is minus 4 theta f of lambda. And this f of lambda is called the CASP anomalous dimension. And you have now connections with integrability, where you can compute this object using integrability. OK, so now if you take phi going to 0, so you have a very small CASP angle. So you stay in your clear case. You take phi equal to 0. And then, of course, you recover in the strictly phi equal to 0 limit, you recover that the Winston line has trivial expectation value at that gamma CASP at any value of lambda in 0 is equal to 0. There is no log divergence. And you can think of it as a wavy line. OK, so this is, of course, a consistency check. And then you can think of this wavy as this CASP contour as a wavy line with a deformation psi, psi dot of mu, which is a step function times phi times a unit normal to the first segment. OK, so if you do that, then you can compute the Bremstrahlung function associated with this wavy line. And then you find that for small phi, this becomes 1 plus beta phi squared log L over epsilon. And so you find that there is a connection between the gamma CASP and the Bremstrahlung function. So the Bremstrahlung function that was introduced from waviness is actually connected to gamma CASP in the limit of small CASP. Actually, there is another possibility that we haven't really considered. Namely, remember that we had the coupling to the gauge field, but also we have the coupling to the scalars. So if you want, you have a geometric contour with a CASP in spacetime and a CASP parameterized by phi, but also you could have a CASP in the internal contour. So you remember it was a theta i, but let's say it was 010000. But then you can consider, OK, since I'm allowing for CASP, I'm allowing for discontinuity, let's say that I've got one coupling to the scalar on this half line. And then after I jump, I couple to a different scalar. So this would be a CASP in the internal space. And you can also do that. And also there are expansions. You can introduce a dependence in this internal angle in gamma CASP. You can expand again, and this is very similar.  So there is a very similar structure. Good, so now we introduce Bremstrahlung function, gamma CASP, you have this. Now you can think about a q-q bar potential as a third object. So the q-q bar potential, you usually think of it as a rectangular contour. So this is how we learn it in quantum field theory. When we study lattice gauge theories, we study Wilson-Lupes in quantum field theory, you think about a rectangular contour with a very long side and a very short side. And so it doesn't seem like we are considering rectangular contours. But think of the CASP actually as a quark. And so think about a CASP that now is pretty big. And think of it as a quark and anti-quark being generated from this point and now propagating. So if you take phi, so this would be phi, so if you take phi going to pi, you have essentially collinear, well, in the limit phi going to pi, you have collinear quark and anti-quark pair. OK, so now you can compute this. So for example, the log. So you can compute this. And then you can introduce the log of w phi, let's say for particles in the fundamental representation, when phi goes to pi, you can introduce some function alpha of lambda pi minus phi log L over epsilon. And so if you compute it at weak coupling, this alpha of L would be like lambda over 4 pi at weak coupling. And it is actually also related to this. And this is essentially the quark anti-quark potential. And it is also related to this gamma CASP. So you can see that alpha of lambda in general is the limit for phi going to pi of pi minus phi gamma CASP lambda phi. So there is this gamma CASP. It's a very interesting function that packs lots of information about different interesting physical situations. So radiation, gram-stallung, and quark anti-quark potential. So you can compute this at weak coupling, but actually you can also compute this at strong coupling because it's a simple surface. Probably I'm not going to give you all the details because. OK, so weak coupling is a trivial computation. You just essentially use the formulas I wrote before and you get this result. At strong coupling, essentially, OK, what do I have? I've got this CASP like this. So this is the z direction. So this is a CASP in the z equal to 0 plane. OK, now I got this infinite, this wedge. And I have to compute a minimal surface associated to this wedge.  It's going to be something like this, right? So it's convenient to use polar coordinates, r and bar phi. And it's clear that this surface has to be self-invient under rescaling, right? It has to be self-similar. So you have a self-similar form. So the answer for this surface is going to be something like z equal to r, some embedding function u of bar phi, right? So this is at the origin, right? And then you tell me, OK, you tell me at which distance you are from the origin. And then depending on phi, I can tell you how deep you are in the interior of the surface. So this is the parametrization. OK, so you write down the Nambu-Goto action.  So you solve it. There is some integral of motion. You have to compute what is the highest point in the surface. Of course, it's going to be the point halfway in the cusp. It's going to be the highest point. So this is your integration constant. Anyway, you can compute it. And so compute action on shell, subtract the divergence and everything, and then you get that gamma cusp is equal to some elliptic integral. So square root of lambda pi u0 square root of 2 plus u0 squared. So u0 is the highest point.  Anyway, you can do that. And OK, you can take the limits now. You can take various limits. So this is valid for any phi. So remember, phi was this angle that I got in the cusp. And phi was the polar angle. So if you take phi going to pi, which corresponds to u0 going to 0 limit, you get that alpha of lambda. It goes like 4 pi squared square root of lambda over gamma, Euler gamma 1 quarter, gamma to the 4 of 1 quarter at lambda equal to infinity. And if you have done exercise number five of the problem sets, you should have gotten this structure from computing. So this was the original papers by Maldesain and Suyam Ray and Yi. They compute this quark-anti-quark potential at strong coupling. But anyway, so you see that everything is related to this gamma cusp. Gamma cusp, as I said, packs lots of information. Then you can take the limit of phi goes to 0, or u0 going to infinity. And then you see that you get the Bremstein function. And this is square root of lambda over 4 pi squared, again, for lambda equal to infinity. So this is a very nice object to consider, this cusp with some lines. Very good. So now, what is the relation of all this study with localization and supersymmetry? Because these are non-super symmetric operators. So should I really only hope that I can compute them in particular limits like I've done so far? And actually, as Diego Correa and collaborators found out, actually, there are exact results that can be obtained from localization for all these quantities. And these exact results have to do with the fourth example I want to talk about, which is this 1 quarter BPS latitude that I introduced in the first lecture, and then it was a subject of an exercise. So the idea is that this B of lambda can be obtained from the quarter BPS latitude. And so a quarter BPS latitude, let me write down explicitly what the contour is going to be in the internal space. So you have a latitude. So there is, you remember, you have the sphere in R4, and then you have the S5 of our symmetry. So you have this latitude, and then you have a dual latitude on the sphere parameterized by this angle theta 0. So you have this angle. So what is called T0 theta 0 here becomes theta 0 here. I guess, well, this is something that we always have to double check 10 times. OK, I'm not sure. Maybe, yeah, it's like this. It's the complementary angle. But I guess it's the other way around. Sine cosine, maybe OK. Maybe I want to write down cosine theta 0 here and sine theta 0. No, I think it was right. Anyway, so you can check that this is 1 quarter BPS if you've done the exercise. And now the fact that it's 1 quarter BPS gives you something very nice, that this width on loops can be computed by localization. And in fact, it is the same matrix model as the usual width. So it's going to be a Gaussian matrix model. The only thing that changes, if instead of adding lambda, you have to replace lambda to cosine square of theta 0. So you can import all the results that you computed already for the half BPS circle to this case of these loops on the S2. OK, so for the particular latitude, you have to do this replacement. For generic loops on BPS2, you have to do another replacement. But it's very simple. So now you can compute this. This, as I said, you can import all the results that you had before. So in particular, we can compute exactly the expectation value of a latitude at an angle theta 0. And for n going to infinity, this is cosine theta 0, some Bessel function square root of lambda cosine theta 0. So it's the same Bessel function. So now, when theta 0 goes to 0, so yeah, actually, yeah, it was the opposite, right? So this is theta 0, and this is theta 0. Sorry about that. So when theta 0 goes to 0, you'll go back to the half BPS circle, OK? And you can see, so the latitude has a wavy deformation of the circle. And so now you can compute the Bremstrahlung associated with it. So you can compute the expectation value of the circle minus the expectation value of the latitude normalized by the expectation value of the circle. And this is, if you expand it for small theta 0, this is going to give you minus 1 over 2 pi squared a Bremstrahlung function theta 0 squared plus dots, OK? So you see from this analysis that the Bremstrahlung function can actually be computed exactly and is given by 1 over 2 pi derivative with respect of lambda of the log of the expectation value of the circle. So this is square root of lambda, Bessel function 2 over 4 pi squared, Bessel function 1, OK? So this is valid for any lambda and n going to infinity, OK? So there is a connection between these four operators. So a wavy operator, a wavy line, a casped line, the quark-anti-quark potential line, so anti-parallel lines, and the latitude. And there are very nice connections that also connect to integrability. So this is an arena where lots of computations can be done, lots of insight can be obtained, OK? So thanks.


The challenge of the Yukon. On King! On your Husky! The Wonder Dog King, swiftest and strongest of Eskimo League dogs, blazes the trail through storm and snow for Sergeant Preston as he meets the challenge of the Yukon. Sergeant Preston was typical of the small band of Northwest Mounted Police who preserved law and order in the new Northwest country where the greed for wealth and power led to frequent violence and bloodshed. But in spite of the odds against them, Sergeant Preston and his Wonder Dog King met that challenge and justice ruled triumphant. The stern face of Inspector Grayson relaxed into one of his rare smiles as the tall, broad figure of Sergeant Preston came into his office. Beside the younger Mountie was a big gray dog that stayed close beside him and seemed to reflect his master's deep respect for the authority of the Northwest Mounted Police. Well, hello, Sergeant. I'm certainly glad to see you. Sit down, won't you? Thank you, sir. I must confess, I worried about you on that last assignment. It was a good job. It took longer than I figured it would, sir. As usual, Sergeant, I'm glad to see you for two reasons. The first, that you got back safely. The second, another job that only you can do. Well, what is it, sir? Oh, this trouble and moose jaw. Five robberies and two killings. It all seems rather mysterious. There are no suspects. Like every town, there's a lot of gambling going on. Three of the robberies were committed after someone had won a lot of money gambling. But the only man who knew about it had perfect alibis. This will be a special assignment for you. Go to moose jaw and stay there until you solve it. Yes, sir. There. Every time I send you out on a tough case, I feel a sense of relief, as if it were already half solved. Well, thank you, sir. Oh, you and that dog of yours. I wish more of our men had dogs like that. Well, there aren't any more like him, Inspector. I'll leave for moose jaw at once. It was a week later that Sergeant Preston entered the general store at moose jaw. Frenchie Le Roux, the proprietor, was an invaluable source of information about the happenings in the town. Hello there, Frenchie. Hello, Sergeant. Well, so glad I am to see you. You just come to town now? Yes. Going to stay for a while. It is time someone come to stop all these crime that go on. That's what I wanted to ask you about. Only last week we have another robbery. Sam Jones. He has $500 stolen that he win at poker. Was he robbed on the way home? No. No, he has to get home and is half asleep. Of course, Sam feel pretty groggy after so much poker and drink. Well, how did the thief get in the cabin? Well, Sam, he think perhaps he don't lock door. All at once someone hit him overhead with lead pipe or something. Of course, it is good that Sam have good hard head that does not break. But in morning all his money is gone.  Who is playing with him at night? Five men play. Let me see. There was... Oh, here is Chuck Adams. He can tell you. Long King. Oh, hello Chuck. Hello, Preston. Say, call off that dog. Say, doesn't he ever forget... Quiet, boy. King does not like you, Chuck. He hates me. Well, Chuck was trying to teach me a wrestling hold a while back. King got the idea of trying to hurt me. He sure did. He took the seat right out of my trousers. And he's ready to do it again every time he sees me. Well, King never forgets anyone who tries to hurt me. I wish he didn't have such a good memory. You staying in town, Sergeant? Oh, well. Good. Hey, Frenchie, those are nice mucklucks. Those green ones over there, how much will they... Yeah, those, those I cannot sell you. I am saved them for Slim Taylor's grandmother. Oh, darn that old woman. Give her time I want something. You're saving it for her. Who's, uh, Slim Taylor? Oh, he is a nice young man who has come to town. I don't share your opinion of him. Oh, what's wrong with him, Chuck? Uh, I can't put my finger on it, exactly. Everybody thinks he's wonderful because he takes such good care of his grandmother. I don't see why he brought an old woman like that way up here. He must support her. Poor woman. She cannot talk. You mean she's mute? Yeah, something happened to her and she can't speak a word. Lost her voice some way. Slim gets away with everything just because people feel sorry for her.  Well, he's either better trickier just because he takes care of her grandmother doesn't mean he's above suspicion. Hello, Frantzine. Hi, Chuck. Hello, Slim. Hello, Slim. Here is Slim now, Sergeant. Slim Taylor, this is Sergeant Preston. Hello, Slim. How are you, Sergeant? Fine, thanks. I have saved these muckluck for your grandma like you tell me to, Slim. Well, thanks, Frantzine. I've got her out in front. I'm a dark sled. Why, uh, it's kind of cold out there for an old woman, isn't it? Well, she, uh, doesn't like to meet people. She can't speak. Yes, I know. How about coming over to the cabin for some dinner, Sergeant?  Well, I'd be glad to, Chuck. I'll see you later, Frantzine. Come back after dinner, Sergeant. Oh, no. It's getting colder, Chuck. Yeah, sure is. There's the old woman sitting on that sled. Your dog seems interested in her. She's afraid of him. Ding! I'm away from her. I wonder if she didn't scare him.  Chuck, uh, I heard you were playing poker with Sam Jones the night he was robbed. Yeah. You mind telling me about it? Oh, no. Not at all. Sam, Slim, and Bart Jacobs, and Sandy McGregor and I were playing. We set a time limit. We were playing the last hand. It was Slim's deal. And on the second draw, I held a pair of aces and drew two more. Oh? Sam had drawn two cards, so I figured him for a full house for four of a kind. Oh, that looked like you and I at the house. It sure did. I threw everything but my dog came into the pot and so did Sam. When we laid down our cards, Sam had the only thing that could beat me. A straight flush. Is that why you dislike Slim? Because he dealt to the wrong card. I haven't said anything about it to anyone, Sergeant, but... I felt ever since that there's something phony about it. I think Slim knows how to deal him like that. Well, that would make sense if he won the money himself, but Sam's winning it. No, but Slim doesn't like me much. I've said things he doesn't like, I guess. What, for instance? Well, everybody thinks he's so wonderful for taking such good care of his grandmother. They give him things and do favors for him on account of it. Like French, he's holding those mucklucks today. You're not jealous, are you, Chuck? I don't think he takes such good care of the old woman. He leaves her alone in that cabin outside of town and plays poker half the night. The night that Sam won all the money, Slim didn't go home at all. He stayed all night with Sandy McGregor. He said he didn't want to walk way out to his cabin. Well, it's a good thing he did. Otherwise, he wouldn't have had an alibi. His grandmother can't talk. Sam was robbed that night. That's right. Did you go home after the game? No, and it's a good thing I didn't, or I wouldn't have had an alibi. Bart stayed with me. He helped me drown my sorrow. Did Bart drink a lot? Sure. Well, I mean, I guess he did. I was doing too well to keep track of him. You're planning any more poker games? We're playing again tonight. Maybe I'll get even. Why don't you join us, Preston? Why, uh, I can't, Chuck. I may leave this afternoon. I have to go to an Indian village north of here. I see. Well, here's my cabin.  I still don't feel safe with him. If you'd stop being afraid of him, he wouldn't growl at you. Stay out here, King. No, you can't come in. About an hour later, Sergeant Preston drew Frenchie into the back room of the store where they could talk privately. Frenchie, I want you to help me. Oui, Sergeant. Oui. I will do anything you say. Spread the word around that I've left town this afternoon. I'll take my team and leave, but I'll be back with King. Oui. There's going to be another poker game tonight. You mean the same people are playing like the night Sam is robbed? Yes. Chuck told me. That Chuck. I do not trust him.  Yes. I've told him I won't be here.   What you do then? I'll go to his cabin and spend the night with him. The same thing may happen that happened to Sam. If the thief comes, I want to be there. Maybe it won't happen like this. It's just a chance, of course, Frenchie. Tell everyone I'll be back in three days. Oui, Sergeant. Oui. I will watch and meet you here tonight. Quiet, boy. It's only Frenchie. Sergeant, you're here? Yes, Frenchie. Is the game over? I leave when last hand is played. Bart Jacobs is big winner. I'll go to Bart's cabin now and wait for him. No worries, Sergeant. They're having drinks for a while afterward. You want for me to go with you? No, I'll take King and go alone. Nothing may happen, but I'll spend the night with Bart anyway. One, King. As Preston and King approached the cabin of Bart Jacobs, they saw no light. Bart isn't home yet. He'll be left his door unlocked. It's open. Come on, fella. As the Mountie entered the cabin, a dark figure was standing near the door. As the big gray dog sprang for the throat of the man who had struck his master, his teeth closed on the lead pipe that was used as a weapon. Get away! King sprang again, but caught and tore only the end of the parker as the man rushed through the door, slamming it behind him. The following morning, Sergeant Preston and King found Frenchie alone in his door. As the Mountie threw back the hood of his parker, Frenchie's mouth opened with astonishment. Sacre bleu, Sergeant. What happened to you last night?  Such big bandage. Somebody was waiting for Bart Jacobs last night in his cabin and got me instead. It hadn't been for King. I might have been killed. Who it was? No, he knocked me out. Bart found me when he came in shortly afterwards. He fixed my head and I stayed there for the night. But how do they know that Bart was winner last night? That's what I'd like to know. Are all the men still there when you left? All but Chuck Adams. Chuck Adams, he gets sick early in the evening. He does not play. So Chuck left early. Did he know that Bart was winning? Bart, he is lucky all evening. King tore a piece out of the man's parker, the one that attacked me. I think I'll go over and see if it matches Chuck's.  You, you are weak. Well, come along if you want to, Frenchie. Oh, I get my parker. One, King. Oh, hello, Sergeant. Hello, Slam. Hi, Frenchie. I wonder if I could get some supplies. You want very much? I must go with Sergeant President. Oh, I won't take long. I'm taking my grandmother over to Selkirk. I'm going to stay with a wife of a friend of mine going on a hunting trip. She's outside on the sled now. Take your time, Frenchie. I'll wait outside for you. Come on, King. Where? What do you want, Slam? Oh, it's a gold dollar. What's wrong with you, King? Help! Get away, help! King, stop! Black boy! Stop him! He's killing my grandmother!  King, like I say, get back! King, give up! Keep him away from me! My grandmother!   Well, this is your grandmother, eh, Slam? Why, it... It is man. He was disguised as a woman. The reason he didn't talk was because he couldn't disguise his voice.  Why didn't you keep still? And that piece torn out of your parka. I think it matches this one in my pocket.  Yes. But King was the only one who knew it. Just a minute, Slam. I wouldn't try to leave if I were you. Well, you haven't anything I can do. You're under arrest. You and your grandmother. But I do not understand. Well, it's clear now, Frenchy. Chuck was right.  He knew who the big winner would be before the game even started and had his so-called grandmother waiting at the winner's cabin for him when he came home. Slam always stayed with someone and had a perfect alibi. It was quite clever. Well, that rotten cur. If it hadn't been for that jogger... King never forgets anyone who attacks me. But hadn't been for King, you'd have gotten out of town safely. This would have been your last job in Moose Jaw, Slam. Now it's your last job anywhere. Isn't it, King? These copyrighted dramas originate in the studios of WXYZ Detroit. And all characters, names, places, and incidents used are fictitious. They are sent to you each week at the same time. Cue-holders speaking, this is the Michigan Radio Network.


Basically what we did here today is a culmination of the efforts and tactical training that we've done throughout the week for the combat readiness course. That's a PACAF requirement that every security forces member has to go through. So we worked with the Korean Air Force and some of the Korean Special Forces this week. We basically trained together as far as fire teams and squad doing mounted and dismounted tactics just to basically see where we were and how we work as a team currently and how we can progress and get better together. Two bullets coming at us! Two bullets! One of our main goals is to obviously put them in different challenging situations, whether they have to clear out a building or they have to move through different fields. So it's just a matter of them actually implementing the proper tactics that they've learned throughout the week. When they take contact, they definitely need to react to contact, engage in the fight, get out of the direct line of fire to where they can actually eliminate off-board. One day we may have to actually work and fight together. Therefore, we need to understand and be able to communicate and be able to provide that joint operations and security.


When the message from my son is late, I get depressed. I can't handle it. And God forgive me, I go mad. The document folder of this Red Crescent volunteer contains family messages, messages which carry so much more meaning than their brief words might imply. They are lifelines, a vital contact between detainees held at the American base in Guantanamo Bay and their distant families. Today, Najib Sultan is delivering three letters written by one of this family's sons. He's been in prison now for four years. When I get a message, I feel enormous relief when the words in it are reassuring. And I cry when the message is sad. I pray to God that he'll be freed and that this will happen as soon as possible. I miss him very much. Getting a letter handwritten by her son is an emotional moment for this mother. She cannot understand why he is being held so far away. I'm really sad and angry that he's over there. Why does he live at Guantanamo Bay? That's why I'm so sad and why I will be all my life. This sense of desolation is also felt in the Al-Hila household. They heard through a message that one of their family who'd been missing for months was being detained at Guantanamo. It's a tough blow for the rest of the family. Our life is difficult and we're sad, especially the children who are still young. They miss their father and they ask a lot of questions. We're living a tragedy. He wasn't only responsible for his children, but for his brothers as well. He was the head of the family. These messages give some reassurance to the families and are moral support for the detainees. Without any doubt, these messages keep his spirits up. They help him to be patient. Even if what he writes is censored, it helps him to express himself. As we say here, a candle in the night is better than total darkness. To be passed on, the messages must contain only general personal and family information. But even without details, families are reassured that the detainees are still alive. Coming from house to house, Najib Sultan continues his rounds. Worldwide, the ICRC has already delivered close to 21,000 messages between Guantanamo Bay detainees and their relatives in 30 countries. These messages have saved us.  We wouldn't even have known where he was for the last four years. I like the work I do. It's very important to find out what's happened to these people who've gone missing. It's a big responsibility. These red crescent messages bring some hope to the families. The situation isn't always easy for relatives to understand. And so the ICRC explains the organization's work in schools. Classes that this teenager, whose elder brother has detained at Guantanamo, follows attentively. The process of verifying the content of the messages can be slow. It sometimes takes several weeks for them to arrive at their destination. When there's no message, his mother and his brother worry. We all worry. We're afraid that he's been killed. We have a constraint which is that the messages have to go through censorship. They have to be read by the authorities. It can be only family news that we bring. But we understand that it's extremely important, even if tiny news, sad news or good news, it's the only way to maintain a lifeline with the family. In Yemen, red crescent family messages are not only used by detainees. They are also a means of communication for civilians separated from their families by war. Rio Harid, for example. Age 33, she's a Somali refugee in Yemen living on her own. The armed conflict and insecurity forced her to flee her village in southern Somalia, where her husband and sons were killed. She's found security in Yemen, but her health remains fragile. For the last five years, she's managed to get by selling small items door to door. Her meager income is not enough to pay the cost of staying in touch with the rest of her family who are scattered in several countries. She turned to the red crescent in Sana'a for help. Family messages have enabled Rio to stay in touch with her sister who's living in a refugee camp in Kenya. She was also able to get news of their father who they'd lost contact with several years ago. I'd love to get a phone call. I'd love them to call me and for me to be able to call them. But I can't. For just a minute on the phone, you can't imagine how expensive it is. I can't afford to telephone. Since the members of the family have scattered, every member is in a corner of the world, so they have to communicate with each other and they have to know their situation. And also, they try to assist each other. Suppose most families in Yemen depend on members of their family abroad. Like most Somali refugees in Yemen, Rio has spent years hoping to go and live in another country. In Yemen, the red crescent passes on five to six thousand family messages every year between refugees and their relatives. Any other form of communication remains a luxury beyond their reach.


to say anything just know that I know that we know that you like myself. So let me find you guys on a hero. No, for some reason we have to like go to our page to find our life being known. Whatever. Okay this is curious about the window. So you guys I am please hold also you can zoom in at just like a teeny tiny bit if you want to you didn't even I don't even thank you. Yeah, this is what it looks like right now. So here's what's going to happen. I wanted to show you guys these these that I did earlier today just messing around with um there's just noises behind me I want to show you guys my these I don't know if you can see them maybe you can tell me if you can see them what's up Jesse Melissa Christine Shannon Veronica hello hello your physical therapist is running behind well I hope it is a good meeting so I want to show you guys these yeah we help me before you go I just want to show them up close the back of this in the front of this I don't know did it focus on the cool detail in the back so I did these and I was like I want to know what I could do with spray paint and then just white resin because that's all I did on these is just put a little bit of white into my resin and then did away so I was like what if I did an awesome background can you believe these are medium I can tell my medicine is wearing off because I'm I've got flight of ideas so um I liked how it looked and then I was like maybe I could paint the background something unique and then just use white and resin to make it do and so that's what I'm going to do in theory so to do this I picked all of these neon-y electric colors I wouldn't dare put this many colors into resin because you all know me you know my standard formula is about four colors so thank you tg to remind people to give their thumbs also hello tg and manamana I think you're the only person and see that gets um a whole song so I'm using Azul Forman Terra I'm sure I said that wrong and this is by Montana in the white can I don't know what this series is about but what's the white can of Montana about what does it mean I don't know it's Montana 94 and then the pink is free and it is by Montana but in the black label I think the black label is like acrylic based but I'm not entirely sure like not enamel based anyways the black is called guess black and the black label the green is called infra green it is also in the black label it's the new infra formula I'm sure infra means no infrared no maybe infrared not interference that doesn't make any sense so fluoro orange is in the 94 can the gold chrome is in the black label and then I have two of these rustolium oh meant to totally meant to do that um rustolium fluorescent cans these are translucent so I always try to throw those in when I'm doing rainbow things because they kind of blend and overlap the colors which I will show you guys in just a moment so when you're working with spray paint where respirator I am not in this moment I have a ventilator running a really big space but um listen to your own body and do what you gotta do if I had a respirator on you couldn't really hear me talk speak and so I'm leaving it off for right now in this moment and I'm just gonna base this a little bit in a white that I haven't shaken yet that's jelly okay I'm just gonna put a little bit of white on here because that'll keep um my brights really bright that sounds like a commercial for a detergent okay so I'm gonna hit the heat gun just real lightly in between the layers of color just to dry it out a little bit if you use too much spray paint in one area it's gonna end up dripping on you I am pouring on one of our rimmed cradle boards I think she just sniffed some I think she just smelled a little spray paint okay and then I'm going to do some green I'm gonna just kind of be loose with the pattern and I'm I know I'm gonna end up overlapping some colors and that is perfectly fine I'm gonna try not to put colors that are opposite on the color wheel next to each other because it's just not gonna be cute just kind of splotching it in just fold it in so letting that blue a little bit over the pink gives me a purple so I'm not using a purple in this because it's really hard to find a brightly colored purple so you can see this yellow is the fluoro rostoleum yellow I am using our spray paint cap so I have more control and I don't have too much air pressure so it's not gonna sputter as much as it would if I was using a different kind of cap if you're worried about sputtering and don't have caps like we have on our website then just have your board up a little bit so that you don't have to worry about it so I'm using this fluorescent to add the yellow color and to give me some secondary colors if I put this yellow over pink it's going to give me kind of an orange in theory and over blue it's going to give me purple in theory I mean not blue not purple it's going to give me green y'all been a day so you can see it gave me the green the orange and some purple and this is kind of just what I used to blend in between the colors and to kind of brighten everything up a little bit but then it gets too bright and I have to tone it down which is fine I didn't get that much orange so I'm just gonna try not to get too crazy with this orange because reasons Bowie you are fine I think you want to put back in some of the brighter green I'm going to end up covering the outside rim in a different color so I'm not that concerned with how that looks I just need to brighten up the blue again the blue is opaque so it can go over anything then I'm going to put the pink and we're going to move on to resin in fact I'm going to go ahead and start mixing my resin so that can be working while we're finishing up this part yes a white teeth commercial so for this project I am using the Illumilite amazing quick coat it is a UV resistant low or no boc quick curing epoxy it cures up in well it's going to give me like 20 minutes to work with it maybe 30 depending on different factors but it doesn't give you long to work with it and I love this thing it's a great resin when you want something that cures really fast and won't smell out your house and has UV resistance it's great so let's do the pink again I don't know if I've done this pink yet actually I'm just going to brighten up things with this pink color awesome all right now that we have those now I'm going to do actually I'm going to dust on first the this some white where my sand is and that is because the chrome colored spray paint that I use if I just put this onto a raw um cradle board then it just soaks in and doesn't give that metallic sheen so I'm going to let that sit for a moment while I stir the edges of my resin I have links down in the description box if you're interested in this resin at a discount it is by Illumilite there's an Illumilite link and Illumilite code down in the description I don't have a link for the spray paints but you can get them at like we get ours from local art stores and head shops a head shop is usually where graffiti artists go or skateboarders sometimes people looking for novelty pipes will go there I'm trying to think of all the things that are there that may like ring a bell to some people not that you guys know about novelty pipes I am comfy I am in my fireball Christmas 1D I tend to wear this thing most days out of the winter months because it's just easy to put on it's like worker overalls and it's warm and I even take the dogs out to go potty in my Christmas 1D no shame I'm okay with it but if you're interested in the caps there on our website artistholdout.com it just makes spray painting a little bit easier and more controlled this I still use stand mixer can be found on amazon I also have a link down in the description and using my link to get to amazon really helps us out here at Artist Hold Us so I'm just going to kind of dust this on so you kind of see some of the white but you also see some of the sparkle from the gold so it looks more of a sheen hope you can see that now when this is all cured I'm going to tape off or mask off the center area where we're going to do our ocean and then paint this outside rim probably black probably so I should be getting a huge order of just resin products coming up soon that is the next order that should be coming in super pumped about that and then next on the list of gonna be delivered is color obsession which means all the tints will be back in stock all right so even if you get one of these awesome I still use stand mixers from amazon using my link um you still have to scrape the sides while it's awesome to like kind of set it and forget it while it's mixing you still have to scrape the sides to ensure that you get a full and complete incorporation of your part a and part b and trust me you don't want to know what happens when you don't get it fully mixed together it breaks dreams wrecks hearts and messes up your artwork so just trust me that you want to make sure that your resin's completely mixed because it's a lot of heartache to have to throw something away that you made oh my goodness okay here we go all right I'm just gonna give it a few more swirls to make sure that we really really mixed everything together I'm gonna turn the light on with you guys and I think I'm gonna zoom you in a little bit so you can kind of more so see what I'm about to do I love this type of ocean wave it's one of my favorites it's gonna be amazing okay I forgot that I needed a little bit of something sparkly and for that we are going to use our milky way slash shooting star however you want to say this is an awesome awesome product it is by resin art you can also get it on my website artistleath.com it looks like a really kind of flaky like a large flake mica but that's because it has this awesome binder in it that gives really cool effects and it's super sparkly and you don't need a lot at all so I'm using probably two of these like a knocked off hope you can see that I feel like a makeup product review person hope you can see that it's not a lot so we're gonna try there just to start and yeah it looks kind of chunky when you start to mix it in let me come over there and show you guys because it's magic but when it's mixed in it's like this most subtle slightly rainbowy sparkle I love it because it's sparkly without being like oh glitter you know what I mean sometimes there's a stigma around glitter and that's fine it is what it is I'm just saying not a concern with this stuff right hey Angie how are you doing thanks for reminding people for the thumbs all right that is going to be way too much for the amount of white we are about to make but it's fine I'm using lures angel white on this but I am currently out in my shop uh a very very close nearly almost exactly identical white is the just resin titanium which I do have in stock until I get my angel white in it's a great product as well it works and looks almost exactly like this one so Christine asked how does this the milky way compared to the abalone shell so the abalone shell is a little bit more rainbowy this has a little bit more of a silver fleck as well as some rainbow whereas the abalone is more rainbow and less um like silvery color okay so I'm going to try to figure out where my shoreline is going to be I think I'm going to come to right here oh my goodness I can kind of see that I kind of let me etch it away a little bit but you guys see that that gives me like ideas to do further etching under like artwork moving forward anyways okay so okay so I'm going to add this along that shoreline that I made and then we're just going to fill it in I don't want to add too much because then it's just going to flow off and I'm going to have an issue when I go to tilt this bad boy later but I'm going to have extra resin if you want to do some coasters you're just going to have to make your decision kind of fast because it's quick coat well essentially if you just want to do clear oceans okay so that's our shoreline and if we want to do multiple layers on this it would be extra awesome so I'm keeping my options open for that now when I add my white for my wave I'm making sure that I'm grabbing both the substrate so it's touching the sand part of my piece as well as the resin or the water area of my piece and that is so that I can kind of stretch the waves that I'm about to make on here it just in my opinion looks super cool when that happens because when resin is just on resin it'll it just kind of glides over itself and doesn't give you really awesome reactions like this will now I feel like my wave shape in this moment is a little bit too like Pepsi nothing wrong with Pepsi no problem with it it's just that's not how a real ocean would be but anyways we can fix that a little later for sure tg one of my go-tos as well so I'm going to use a heat gun on half and a torch on half just to show you what the difference is so I'm going to try to zoom in the opportune areas I'm just going to tilt that resin back this way that tilted forward when I was showing you guys all right so I'm just going to do this bit right here with the torch just so you guys can see what that wave looks like in comparison so I heat it at first and I just kind of give it a little bit of motion using your face and then I heat it just a little bit more with a torch to get those cells to pop up and that is how I do a torch and tilt wave now what I usually do is use my concentrator nozzle which you can find on our website and a heat gun that has a really good amount of air flow and what this concentrator nozzle is going to do is kind of make a ripple kind of what this looks like since I did like the first breath and then the second breath if you want to not try to faint in your resin this is a great option this is actually on my website the groom's cake it's kind of a larger hole in the front whereas I have a wedding cake that has a smaller nozzle in the front and that'll give you more ripples so just like with the torch and tilt I'm going to get mad at my heat gun for not going on okay there we go and I'm gonna preheat just where I'm gonna be working and I'm gonna just do little circles till I see it start to move little circles till I see it start to move and then I'll kind of trail it out a little bit into the wave to kind of keep it moving and I'm just going to do this side is a little bit as well to kind of just marry those two ends together and I'm not going to stop it because then it'll mess up what I'm doing here but I think I like the other side better than the torch and tilt so I'm just going to try to catch this side up with the first side I'm going to have to use a torch on this area down here but that's not a problem huh how fun so this area here that's kind of how can you guys see this better okay yeah so this area here that doesn't have as much white in the forefront is because I didn't put enough white in front of where I had my clear and so it just rolled over the top and only grabbed a little bit if I didn't have anything touching the sand then it would have just rolled backwards and if I had more touching the sand it would have been like this and this it's really hard to fix that at this juncture so I'm just going to kind of edge up my wave a little bit and then we can fix this bit during this second wave which I won't be adding today because it's my opinion that you should wait till your piece is cured to do a second wave I'm just going to touch this area with some heat a little bit and try to get it to disperse some actually that reservoir is full so I'm going to try to roll it around so I can fill up more of the reservoir and actually I think that looks okay I think it looks pretty cool and I have a little bit of resin left over so I'm going to see what all I can do with it before it starts to cure since it is the quick coat so I have another piece here hopefully I can get it unwrapped before my resin cure is on us I'm going to be cutting it close fam let's race against the clock that I'm not prepared for but we'll make it work anyways so I'm using one of our clear clock substrates let's turn that light off to give you guys a better view a little bit all right so let's do wave so what you do with our clear shapes is you take the backing off of one side put resin on that side and then once your piece is cured then you take the backing off and you don't have any cleanup and it is just such a time saver and you can get these from our website artisle.com okay we're just going to do all a heat gun wave on this one sorry I'm not reading the comments I'm trying to not waste resin we'll just do this a couple times see what that looks like cool all right here we go it's going to tilt it a little bit preheat it tiny circles and since I have three kind of waves I have to work it down a little bit more than I usually would have oh no it might just take over I may have just done too much of the clear well let's just tilt it around and see what happens actually I think that's gonna look really cool where's the oh it's stuck to it I may have time to do one more it's amazing how not a lot of product you can end up using and still come out with really awesome artwork I'm mixed in the beginning I think eight ounces and I've done a 15 inch round that clock is 12 inch and we're about to do another 12 inch piece that is if I can get this paper off in time I cannot wait to take the backs off of these tomorrow it's like Christmas morning without it even being Christmas morning basically yeah so I'm gonna give you guys a better look at these that's not gonna work after I get them all done let's make a deoid so let's wipe all that off I'm gonna start with the whites on this one because it's going to dictate kind of where the clear goes this is kind of kind of be like an island in the center and then the clear water around and then if we end up liking the piece and we can just spray paint the back any color that we want after we look at it in its completion and I think that's super cool okay white check okay some of my clear has rolled over my white right here so I'm gonna have to fix that because we won't get as great of cells just right in that area the white needs to be on top this is a top cell white it is not a base cell white I have plenty of base cell products on my website if you are into base cell activators but today it's all about the top cell if you guys want just let me know down below if you want me to do a comparison video of top cell and base cell whites or just paste in general I've also been thinking about doing another comparison video of all of the types of colorants that you can use in resin with that interest y'all let me know I am so on the clock with this quick coat thank you guys for being patient with my being able to read comments currently here we go typically I've put the pieces on tilt I don't know if that's gonna really work with this one because we're gonna be going all the way around tiny circles I'm just using my face to kind of blow out from the center I thought for a minute there I was gonna pass out a little bit but we made it so it looks a little bit doughnutty right now so I'm gonna kind of just try to blend out some of these edges so it doesn't look quite so consistent all the way around and to do that I'm just heating the edge and trying not to pass out I mean blowing out until it disperses same same now when using a torch you have to be very careful not to scorch your resin it is very easy to do if you see it move pull back your heat if you see it smoke hold your breath and then move your whole self because it's going to smell horrible even no VOC epoxies will have an odor and release chemicals if you scorch them and on top of you know noxious get not noxious and not noxious on top of just not fun smells permeating from the resin you could end up with like a scab like finish because that's what it looks like when you scorch your resin ooh I'm really liking this I want to do a bigger one should I do a bigger one yeah let me know if you tune in for me doing a bigger one and I'll tell Jeff that I need a bigger geoid it's going to be quite a scramble to try to get a large piece done in the amount of time that you have to work with the amazing quick coat but it'll be fun to watch I imagine I love how this looks I cannot wait till I can take the backing off and show you guys what it looks like just clear and amazing hi recovering foodie I will absolutely do a comparison video an updated comparison video on the different types of colorants I do have some already on my channel but it doesn't have all the available colorants that I know of on there and so I will definitely do a new one for you guys because I do think it would be helpful I'm doing my best not to pass out top versus bottom I see you Jesse um yes cat it is awful when you inhale scorched resin right I should use Jeff's face to to do this but his face is all the way in there I think he's taking a shower so let me show you guys what this looks like up close and personal how fun focus can you focus no not gonna okay there's some how fun are those cells you can get those cells from using um uh today it was angel white from lores but I am out of that color at my website artistledeath.com so you can also use um just resins titanium white which is also on my website and the sparkle in the background is the milky way or shooting star also on my website it is from lores here's our white round ocean on a clock there's a very angry ocean but I love the difference in like tonality because of all the different layers of white we did nice nice and then our rainbow those cells really grew into themselves didn't they even our interesting little torched ones ooh those are big let me just show you the size of these ones so here's the end of a popsicle stick that's a big cell and those are the coasters we did yesterday boi says hello apparently so yeah I hope you guys enjoyed this video boi enough I'm super excited to do that new um comparison video for you guys hopefully I'll have the latest crime and craft up this week I've been hit with the sickness okay calm down I've been hit with the sickness so I haven't been uh at 100 to finish editing that but we'll get it done this week boi thank you and enough so anyways um yeah I think I'm gonna do a bigger one of these because I really want to highlight what you guys can see really this like ripply looking actual texture looking texture that's not because it's behind because that's the bottom side of this piece that just I feel like there's a way I could harness this look and I haven't found it yet but I'm going to going to with y'all's help anyways you see there's any questions um I haven't answered uh you guys are so amazing thank you tg for adding those links you are the absolute literal best and I don't have anywhere to put this so it's just gonna live right here tell it cures which won't be long it'd be a couple hours because I use the quick code anyways is it possible to layer the clear bases together to create a 3d effect uh yes yes you can I was doing there's something similar to that yesterday so we did these coasters yesterday and I was showing people that you can absolutely layer them together you can just I would use e 6000 or the standoff wall um mounts they just go in the low corners and you can get clear ones and yeah just pretend this part is clear and then it looks great but yes you can layer them yes they look amazing yes I am biased and in case you missed what the white also does when it sinks through other colors it makes this like feathery look when when it's laying on like a surface like our clear ornament shapes um it kind of pools in these little shapes that I super love Melissa yeah you can put translucent blues on the other side if you don't even want to use resin you can just use paint but yes absolutely you can do that the shapes are very versatile and if you want a custom shape or size just shoot me a message um on the website and I'm happy to have Jeff cut them for you now this is unrelated but have you done any emerald or jane stone color projects I've done many emerald and a few malachite life of dan and I'm happy to do another one are you looking for something that's um like clear like a geode or something that's more like um a countertop type finish either way yes I'm happy to do one I just need to know which one so I can prepare my colors and etc so Bowie wanted to say hello big boy Bowie where are you yelling at yeah my precious boy okay she came in like a wreck and off um countertop I'm the guy who made the marble guitar well you're probably oh yeah I do remember you um if you guys haven't seen Dan's guitar I don't know if you have it on social media or YouTube specifically but it's pretty rad um I will absolutely do an emerald or jade countertop absolutely listen I may be a space cadet sometimes I may be forgetful the rest of the time but I make it a point to remember my clients my customers and my fam my subscribers and all the people that reach out to me for anything at all ever well I can't wait till you do Dan because it's pretty amazing all right you guys I have to take these two out because canvas is starting to rip apart her puppy and yeah I'll see you guys tomorrow thank you for covering foodie I hope you guys enjoyed it if you haven't subscribed yet please do so leave me your thumbs and recommendations on what you would like to see on our channel down below and we'll see you guys next time be kind of one another because you never know what someone's going through and I always remember that we do the test you don't have to and we'll see you guys in the next video canvas stop ripping apart your bear canvas no ma'am all right guys bye