I put some formulas on the board from the previous lecture. So just to review, so the classical action for the string has px, and it also has two sets of pure spinners and the conjugate momentum, which I call lambda alpha and lambda hat alpha hat. And alpha and alpha hat are the same chirality for type 2b opposite chirality for type 2a. And then you have these constraints, which instead of just having p slash lambda, for lambda, you have the constraint p slash plus d sigma x slash. And for lambda hat, you have p slash minus d sigma x slash. So these are supposed to replace the p minus dx and p plus dx squared, the left and right moving. And you also need to introduce these additional constraints for the sigma derivative of lambda and lambda hat. So that's just to get the algebra of these first class constraints to close.  Furthermore, it's convenient to do a shift to get to the first order form where you don't have p's and you just have x's. You do a shift of l and k so that you generate the usual coupling of the Worldsheet via brine, which you can encode in just two Worldsheet fields, e and e bar. So these are the Lagrange multipliers that multiply the left and right moving via a Zor constraint. So this is just like in Bosonic strings here. So t is just as the contribution from x, and it also, of course, has a contribution from the lambdas. And there's a similar expression for t bar. OK, so this shift will be j is w. This shift of l and k is just what generates these terms in the stress tensor where e, this e here is the same e as here. And there should be an e serian. OK, there are any questions on this? So this is the classical action. Then we gauge fix it. I'm not going to go through the gauge fixing. Again, we land on this pure spinner action. It's just a quadratic action. So these are the left movers, and these are the right movers. The thetas come, of course, from the Lagrange multipliers for l and l hat. And the resulting BRST operator has this form. So it's manifestly space time superponkering invariant, where d alpha is the same constraint as you had in the green Schwartz formalism. But now it's not imposed strongly. So p is now an independent Worldsheet variable. It's not defined in terms of the d alpha equals 0 constraint. And the d alpha and d beta satisfy this OPE, where pi m is now the supersymmetric version of x. So you can show the q squared equals 0 using, of course, that lambda gamma lambda is equals 0. And you can construct vertex operators in the cohomology. So this is the unintegrated vertex operator of ghost number one for the open string, where this super field when qv equals 0 describes on-shell d equals 10 super Yang-Mills. And the integrated vertex operator of dimension 1, so this is, of course, conformal weight 0, because all of these fields have conformal weight 0. This has conformal weight 1, because d theta, pi, d, and n have conformal weight 1. And it obeys this relation. So the BRST variation of the dimension 1 field is the world-sheet derivative of the dimension 0 vertex operator. OK, and these here are the same as d alpha and pi m that appear here. And n is, of course, the Lorentz current for the pure spin. OK, so any questions on that? So that's the review of what's called the minimal pure spin of formalism. And there are two things we learned when we were trying to do this gauge fixed description of the pure spin of formalism. One thing we learned is that the tree-level measure factor needed regularization. So that's just because of the non-compact lambdas. So they're no longer projective pure spinners. They're now ordinary pure spinners, because we've fixed the scale symmetry. So they have non-compact degrees of freedom. And when you integrate over them, you get divergences which need to be regularized. The other thing we see when we did this shift is that we have to introduce this field lambda bar. Now lambda bar can be anything, because you're going to divide by lambda lambda bar. It's easy to see that this shift reproduces this for any object lambda bar. But of course, lambda bar breaks Lorentz invariance. It's a spinner. So if you fix it, of course, any Lorentz transformation that changes the value of lambda bar will not be a symmetry of the act. Not the symmetry of this shift, at least. So it will be convenient to introduce a worldsheet variable which is going to play the role of this lambda bar. So fixed lambda bar breaks manifest Lorentz invariance. OK, so we're going to solve these two problems simultaneously by what's called the non-minimal. So the idea is we're going to add to the action some new fields, which I'll denote by w bar alpha, which will be a set of bosons. These will be bosons. And these will be fermions. And I'm going to introduce an equal number of bosons and fermions so that I'm not going to affect, for example, the central charge of the conformal anomaly. And of course, you also should introduce the right moving analog of that. So these are left moving, and these are right moving on the worldsheet. And in order that they don't contribute to the chromology, we're going to define the new BRST operator, which I'll call q tilde, so let me just call this S tilde, which is equal to q plus the new term. It's going to be defined to be w bar alpha r alpha. So using what's called the quartet mechanism, one can argue that if you add, of course, also to the right moving BRST operator, you do something similar. One can argue that adding this term implies that the physical states will, any dependence on these fields that respects the fact that it's annihilated by this operator, can be written as something BRST trivial. So you can remove from any physical state dependence on these worldsheet variables. So they're not going to spoil the chromology. You're still going to get the same super string spectrum as before. But the advantage is now we're going to be able to covariantize what we're calling this shift. And we're also going to be able to regularize this tree level measure factor and also measure factors associated with the hyogenic surface. OK, any question? OK, now one can ask a question, can we get this from gauge fixing, this action here? And you can. What you have to do is you have to introduce the non-minimal variables already at this stage. So you introduce just the bosonic ones. And then you introduce a constraint, which is essentially a trivial constraint. It just tells you that, sorry, I'm running out of space, which is going to be just a Lagrange multiplier, let's call it h, times w bar alpha. And the hat inversion, h hat, alpha hat. Now when you gauge fix this Lagrange multiplier to zero, you'll generate ghosts. The ghosts will be precisely these r and s variables, and r hat and s hat variable. So one could have done this from the beginning, starting with this classical action, introducing the non-minimal variables, but in order not to introduce lots of notation, I saved it for this gauge fixed action. But if you want, you could have introduced them from the beginning. And of course, introducing this gauge fixing, gauge fixing h and h hat equals zero, or r are the ghosts who are going to generate these terms in the BRST operator, because the constraints are, of course, w bar and w bar hat equals zero, and these are the ghosts. So this is the usual ghost time constraint. So it looks very trivial, because you've introduced something, and then you've constrained it to zero. But it's going to be useful, as we'll see. OK, is there any question? OK, as you can guess from the name of it lambda bar, they're also going to be pure spinors. So I'm going to require that lambda bar gamma m lambda bar equals zero, which means that this also has 11 independent complex components. Notice that the alpha index means that it's lowered, so it's antiviral as opposed to lambda, which was vial. And if I want this to be the superpartner of this lambda bar, not to introduce new degrees of freedom, you also need a constraint on r. So the constraint on r is going to be that this combination with lambda bar is going to be equals to zero. OK, so this implies that both lambda bar and r alpha have 11 independent complex components. If I want, I can solve the constraint by choosing a u5 subgroup of s o 10, but I'm not going to go through that unless it's a question. Similarly, of course, you do the same for lambda bar hat and r hat. OK, any questions? OK, so now let's see how this helps. So let's go back to computing the tree amplitude that we computed before. So remember, the tree amplitude was computed by having three unintegrated vertex operators and n minus three integrated vertex operators. And this involved an integration over 10 x's, 16 theta's, and 11 lambdas. And this meant that you got an infinity to the 11th. Now, of course, we're going to integrate over the lambda bars and the r's. There's no integration over the conjugates because the conjugates have confirmed weight 1. These are all confirmed weight 0. So the conjugates don't have any zero modes on a genus zero surface. OK, so it looks like you've just made the problem worse because now you have more non-compact integrations. But now one has the freedom to modifying the gauge fixing condition. So the gauge fixing condition to start with, remember, was of the type p alpha l alpha plus, I didn't go into the k, but there's also a term kl. Now one is going to add, OK, there's also a gauge fixing associated with gauge fixing h to zero. So that will be r alpha h alpha. So that's the usual terms you would expect from the gauge fixing we just did. But now I'm going to add a new term to the gauge fixing condition, which will be minus lambda bar alpha theta alpha. And I can put an arbitrary coefficient in front, epsilon. Now this, of course, may look a little bit unusual, but I'm allowed to choose chi however I like. And if this helps me to regularize, it shouldn't change the answer. So what does q chi? So of course q chi from this stuff is what we had already. You get, well, this term here, I'm not going to go through this term here, it's a little bit messy, but it's in the paper that I mentioned. Here you'll, of course, get the term, this should have been an s, sorry about that, s d bar r.  That comes from the BRST variation of theta. And you'll get another term from the BRST variation of lambda bar. So if you look at this BRST operator, you can see that q lambda bar is going to be equal to r alpha. That's one way to see why you need this constraint, because if you take q on this, it had better be 0. So this obviously follows from this BRST operator because lambda bar is the conjugate to w. So you get an extra term here, which is plus r alpha theta l. Now if we use this gauge fixing condition here, then of course when we exponentiate it, the action, so we have a term of course the exponent of the action, which is going to now have this q of chi here. Now this is going to be equal to e to the minus s c.  Now it's easy to see, this gives a Gaussian cutoff for the lambdas. So you no longer get the divergence. So we have these objects we have to compute. But now we have a regularization. So we no longer get infinity. And in fact, this also is going to kill some of the fermionic zero modes. Now if we use the v's and u's that are described here, there's no dependence on the non-minimal fields. So in order for this to be non-vanishing, you obviously need to get 11 hours. The 11 hours can come from this exponential. So this is going to give me, so you get these integrals as before. Now pulling down this factor here, you're going to get a factor of epsilon r alpha theta alpha to the 11. Multiply it, of course, by exponential minus epsilon lambda alpha lambda bar alpha. And you integrate that over d 11 lambda d 11 lambda bar. It's easy to see that this Gaussian integration is just going to kill, you're going to get a factor of 1 over epsilon to the 11 coming from this Gaussian integration, which is going to kill this epsilon 11. So for any value of epsilon, as long as, of course, it's not zero, you get the answer is going to be independent of epsilon. So this is going to give you a regularization. OK, so now we can, of course, do the integral. We have v1, v2, v3 times these u's. Now we still have to do the integral over 16 theta's and the integral over 10 x's. But now you see 11 of the theta's have been absorbed from here. So this is effectively going to give me just an integral over 5 theta's. And one can work out the Lorentz indices. And you find that the answer is precisely this expression we worked out yesterday. So if this can be written as lambda alpha, lambda beta, lambda gamma, f alpha, beta gamma, after doing the integral over all the non-zero modes, you find that the zero mode integration just reproduces precisely what we had yesterday. OK, so this is a functional integral method for obtaining the answer we had yesterday. OK, any questions? OK, so this method is straightforward. And now the next step is OK. We think we understand tree amplitudes. As I already mentioned, this was already shown to agree for all the massless endpoints scattering tree amplitudes. You can, of course, also do massive. There's no restriction of doing massive. The only difficulty is these vertex operators get more complicated, because instead of just being dimension one at zero momentum, now there'll be dimension two or dimension three at zero momentum. So you'll get more and more of these worldsheet fields involved. But in principle, you can work out these vertex operators and compute any tree amplitude in this way. OK, the next step, of course, is do loop amplitudes. So the first thing one has to figure out is what's the correct prescription? So on higher genus surfaces, let's say genus G, it's no longer possible to gauge E and E bar equals zero. So the gauge fixing condition came from gauge fixing. So we have to gauge fix E and E bar to zero to go to conformal gauge. That's essentially gauge fixing the worldsheet metric, H ij, to be proportional to delta ij. On higher genus surfaces, there are global obstructions to this. So their global moduli are left over, which are just the Teichmühler parameters. 3g minus 3, complex moduli, which I'll denote by tau p. So p is 1 to 3g minus 3. And what this means is that the gauge fixing condition chi equals b. So if you're doing bosonic string theory, what you would do is just gauge fix E and E bar to zero, which would be done by introducing the gauge fixing fermion, which is just b times E plus b bar times E bar. So this is just the usual bc ghost and b bar c bar ghost. And these are the anti-ghosts which multiply the constraints to set E and E bar equal to zero. So this is bosonic string theory. Now, if you cannot gauge E and E bar to zero globally, that means you're actually doing too much. So some of these b and b bar anti-ghosts are not doing what they should be doing. Because in some sense, you're introducing too many b's and b bars. So what you have to do is you have to set some components of b and b bar to be zero. So the way to do this is by introducing a Beltrami differential, which I'll call mu. So these are Beltrami differential, which are going to be dual to the choice of these complex teichmühler parameters. So for each global modulus, you have a Beltrami differential, mu p, which you can use when you contract it with the b ghost. These are essentially the modes of the b ghost which you don't want. Because some of these modes of the b ghost are gauge fixing things which can't be gauged away. So you have to get rid of those modes of the b ghost, which is done by inserting these delta functions into the scattering amplitude prescription. Of course, similarly for the b bar ghost. So this is one way of understanding this genus G prescription where these b ghosts in the prescription enter. So the prescription for Bosonic string theory for genus G, you have an integration over these 3G minus 3 teichmühler parameters. And then you have a genus G correlation function. And in this case, you don't have any conformal killing vectors. So all the vertex operators should be integrated. Let's assume genus G bigger than 1. But then you have to explicitly insert these delta functions. So you have 3G minus 3 of these insertions. Of course, the delta function of something fermionic is just the object itself. So this is just equal to mu p. So this would be for the open string. For the closed string, of course, you take the left right product. So this would be an endpoint amplitude prescription for Bosonic string theory. Are there any questions? So now we want to do the same thing for this, for the pure spinner. Now in this case, we have a different chi. We have this more complicated chi. I guess I wrote it down here. And now we're going to do a shift of the L's to see exactly which terms in chi coupled to e and e bar. So it's easy to see what happens after you do this shift. You generate some new terms. So you have e times, so here I wrote down the shifts.  So that comes from the shift of L. And you also get a term from the shift of k, which is of the form N mn gamma mn lambda bar. So of course, the coefficients here I'm not being careful with, but of course, this is all in the reference. OK, so this object here is going to play the role of this b ghost here. So if you do things more carefully, you find that so here you're going to get something I'll call capital B because it's not the fundamental field. And it has the following form. I guess I'm going to use this later. So capital B turns out to be equal to I m. We're essentially what I've done is just read off the terms from here. There's some extra theta dependence which makes this spacetime super symmetric. And it's easy to check that qB is equal to t, which is equal to, you can write it in super symmetric language as minus 1 half pi m pi m plus, I guess, minus dL. So it has the same structure as you had in Bosonic string theory that just like q with small b is equal to the Verizor constraint in Bosonic string theory, q with b is equal to the left-moving stress tensor in pure spinners. But of course, this b was defined using the minimal formulas. So it explicitly involves the lambda bar and it's not Lorentz covariant because you fix lambda bar. Fortunately, one can define now a b which is fully Lorentz covariant by using instead of q using q tilde. So I shouldn't have erased it. So q tilde was this thing plus w bar r. So you can define something called b tilde, which is equal to b, plus some other terms which will depend on the non-minimal variables. So these will be crucial when you compute the loop amplitudes. And these are the extra terms you need to add. So it will look like a mess, but the structure is required in order to write something which has the right BRST property. So this should have been. And one can show that this b tilde satisfies the property that q of b tilde is equal to t tilde, which is the same as t, but of course, plus the contribution from the non-minimal field. So these terms are required because of course, b does not commute with w bar r because it has lambda bar dependence. So you need to add other terms in order to cancel that dependent. Now there's a good feature and a bad feature of b tilde. The other good feature is, of course, it's manifestly 10 dimensional super Poincare invariant. But it still has the unpleasant feature that has poles when lambda lambda bar equals 0.  So if you have enough poles in order to cancel that 0, so lambda lambda bar to the 11th comes from the measure factor. And then from each b ghost, you can get a factor of 1 over lambda lambda bar. The maximum it can give is 1 over lambda lambda bar to the cubed. You might think it's 1 over lambda lambda bar to the 4th, but you see there's a lambda bar in the numerator. So each b ghost can give you this. There's 3g minus 3b ghost on a genus g surface. So you see this can diverge. g is greater than or equal to 3. Now it doesn't have to diverge because it's possible that these terms won't contribute. But if you go to a genus 3 loop amplitude and you ask for the amplitude with arbitrary factors of alpha prime, so you try to do the full genus 3 loop amplitude, you will run into problems. Now I told you in the first lecture that Gomes and Marfa computed the 4.3 loop amplitude, but they computed just the lowest order in alpha prime. So they're actually able to extract the coefficient and prove that it was consistent with estuality. And their computation only used factors in b that had fewer than this number of poles. OK, so this is an unsolved problem in the formalism that at the moment, if you want to compute for arbitrary g loop, one has to regularize the divergence when lambda bar goes to 0. There's a proposal for how to regularize it by myself and Necker-Soph, but the proposal is too complicated to actually use it in explicit computations. OK, but in any case, what I'll now show is how to do the computations, at least for genus 2 and genus 3. And we'll see, I can do it in 15 minutes. And I would challenge somebody using RNS formalism to try to do this in 15 minutes. OK, so any questions? Good question. OK, so the way I'm doing it here, all the vertex operators are integrated. One could ask even for tree amplitudes. OK, good. So the question was, there are different ways of parameterizing a sphere with n punctures. So let's just do a tree amplitude, which are essentially the choices these mus.  So what I've done here is I've associated the n of the complex moduli with the locations of the external states, but that's not necessary. And what he's asking is, if you choose a more general parameterization of the punctures, will you be able to compute? Because in that case, you will get, even for a tree amplitude, you will have to insert, well, it will be n minus 3 b ghosts. So that has not been worked out. So you would run into this problem already, a tree amplitude, if you tried to choose a different parameterization. So that's an excellent question. And in fact, one can check this regularization that I proposed with Necrossov, even for tree amplitudes. And that has not yet been checked just for the reason I told you that it's too complicated to do explicit computation. Any other question? OK, so let's do the loop amplitudes. So the first thing we need to do is to generalize these integrals now when we do loops. So of course, one now has to do integrations not over the zero modes of the conform weight zero objects, but over the zero modes of the conform weight one objects. So with genus G, now we have w alpha, w bar alpha. These both have 11 g zero modes, because there are 11 components of each. And conform weight one object have g zero modes on a genus G surface. These, of course, are bosonic. Of course, you also have the s alpha. So those are the conjugates to r. And you have the p alphas. So these also have 11 g, but these, of course, are fermionic. And p alpha, of course, you have 16 g, because there's no constraint on the p's. So you have all 16 components. Now these, of course, are bosonic. And these are fermionic. So the first thing you have to do is to regularize the integration of the bosonic. Because now you'll still get, just like you've got infinities from the non-compact lambda zero modes, now you'll get infinities from the non-compact w zero. Unfortunately, there's a term you can add to chi, which also fixes that. So the term you'll add, of course, if you have g zero modes, let's use the letter r to label the different zero modes. So in other words, I'm using the notation where on a genus g surface, for example, p alpha, you can write it as some times the holomorphic, I don't know what letter to use, but they're g holomorphic one forms, which I'll call omega. And, of course, I can decompose p alpha in terms of them. So these are the g zero modes that I will have to integrate over. OK, so I'm going to add a term to chi, which is going to regularize the integral over the w's and w bars. And the term will be given by s alpha w alpha. So that means that q chi is now going to pick up, of course, it still has this term, which was, I guess it's going to be minus here, minus epsilon. That's going to be as before.  So what we've used is that the BRST operator, of course, it takes s alpha into w bar alpha, because r is a conjugate momentum to s. And furthermore, it takes w alpha into d alpha, because of this term here. OK. So this term will take w alpha into d alpha. So we get these two terms as before. We get this term which regularizes the Bosonic divergence, and this which gives extra fermionic zero modes. OK, so now we have to do the integral over those also. So we have d 10 x. Now we have d 11 g w, d 11 g w bar. d 11 lambda, d 11 lambda bar. Now we have the 16 g p's, 11 g s's, and the original zero modes. So the original zero modes of the conformity zero field, we have 16 theta's and 11 r's. So this is the integration we need to do. Now when we compute q chi, we have this term here, but we also have this term here, epsilon r w w bar plus s d. OK, so let's see what we can get. Now, of course, if we don't have enough fermionic zero modes, the amplitude vanishes. So we just have to count the zero modes. OK, so the computation we're going to do is the four point genus two and then the four point genus three. OK, so we have this u 1, t u n. The fermionic zero modes here can come from various places. They can come from the exponential here, or they can come from the vertex operators. So the vertex operators are defined here. So there are also some fermionic zero modes here. Or they can come from the b ghost. So this b ghost here, you have 3g minus 3 of them. So they can also contribute fermionic zero modes. So now it just becomes a counting problem, at least to see if the amplitude vanishes or not. It's trivial to show, for example, that if you have less than four external massless states, the amplitude vanishes. So in order to absorb enough fermionic zero modes, you need to have four external massless states. And that, of course, is crucial to prove these finiteness theorems. OK, so let's do the two loop first. So for g equals 2, we need to get 32 p's. So we need p to the 32. We need to get s to the 22. And then, of course, we need theta to the 16 and r to the 11. So the question to all genus is the question you have to ask about these 1 over lambda lambda bars. So what you have to be careful about is that when you compute these, let's say, three point amplitude, that you never get these divergent contributions coming from the lambda lambda bars in the b-ghost. So there are arguments. I think it depends on your rigor if you call it a proof or not. But certainly, if you ignore the question about the 1 over lambda lambda bars, then it's a proof. So the 1 over lambda lambda bars, you have to either use this regularization, or you have to argue that they don't contribute. So there's an argument, but I'm not saying it's a proof. So let's look at the genus 2. So the genus 2, we have to absorb these zero modes. So let's first look what can come from the exponentials. So from the exponentials here, you can get an s. So d alpha essentially gives the zero modes for p, because d is essentially p alpha plus something else. So you can get for free sp to the 22 coming from this exponential here. Because this is a sum from r equals 1 to, well, there are two g of them. And there are 11 s's and 11 p's. So for each, sorry, 1 to g. So when g is 2, you can get 22 factors from here. And of course, again, you'll get from the Gaussian integration over w, w bar, the epsilon r will drop out, the same as it did for the epsilon. So that killed the s zero modes. One still has the r and theta zero modes. And one still has 10 of these p zero modes. So in this case, one has 3g minus 3b ghosts. So one has 3b ghosts, so b tilde cubed. And the term which is most useful in b tilde for absorbing zero modes is this term here. So this term here has two p's and an r. You can get fewer p's from the other terms, but this is the unique term with two p's. And it will turn out that for four point amplitudes, the only term that contributes from the b tilde is that term, just to absorb the p's.  So now you see you get six p's from here, 22 from here. You're still missing four. Unfortunately, you still have the vertex operators these use. And each u can give you one p from this term here. So that's the simple argument that the amplitude vanishes for less than four external states. You just don't have enough p zero modes. So from the vertex operators, u cubed or u to the fourth, you pick up a pw to the fourth. And now you can see you're still missing the r's. So you're missing eight r's, which are going to come now from this exponential here. So in principle, this could give you up to 11 r's. We saw for the tree amplitude, this gave 11 r's. But in this case, we already have three of the r's. So we only need to get eight more. So that pulls down eight theta's. We need to have 16 theta's. So that immediately says that the amplitude is going to be proportional to d to the theta to the eighth of the w vertex operator. So we have w to the fourth. These are super fields here. And of course, these super fields depend on theta's. So these are the only way to get theta's zero modes is from the vertex operators or from this exponential, because everything else is superpunk ray invariant. They can't contribute theta's zero mode. OK, so this is the answer you get. This is the term of lowest order in alpha prime. And if you expand it in components, each w has to give you two theta's. So that turns out to go like d squared after the fourth. So just by dimensional analysis, it's easy to see that. Right. Now, this is for the open string. Of course, if you do the closed string, you just get the square of this. So it goes like d squared after the fourth squared, which in closed string notation is d fourth out of the fourth. Now, of course, you can work out the index contractions. It's a bit of a mess. It was mostly worked out by Carlos Mafra. So the superspace expression is trivial to write down. So you're just writing down the w's, but doing the integration of the theta's is a bit of a mess. You need some mathematics or something that can handle lots of theta's. He's worked out all the programs, and he showed that this index contraction is, of course, precisely what you want. And furthermore, together with Mafra, together with Gomez. So this is in 2010, they computed the coefficient here. Now, the coefficient was computed using factorization in the RNS computation. But in some sense, it's not a computation. It's a one-loop computation, which essentially you take the square of. That gives you, by factorization, the two-loop coefficient. But it wasn't the direct computation of the coefficient. In fact, it's not known how to compute this directly. In RNS, just because, as I mentioned in the first lecture, you have to compute determinants of fields of different conformal weight. Whereas in this theory, all the fields here are either conformal weight 1 and conformal weight 0. And just because the central charge cancels, the contributions from the determinants also cancel. So there's no determinant computation that you need to do. So that's what makes this computation. It just comes down to a computation of zero modes. So you just have to know how to do the zero mode. So D11 lambda, I wrote down the expression. But of course, lambda is a pure spinner. So you just have to parametrize SO10 over U5. Just have to. This is essentially what Umberto Gomes worked out. How to do this integration over SO10 over U5 variables. So it's a computation that was done. And they found this coefficient and showed that it, of course, had agreed with the dokerfong, which agrees with the s duality conjecture. OK, so three loops. Again, it's just algebra. Now you're going to get in 32. You're going to get 48, s33, theta 16, r11. Now you're going to get sp to the 33, coming from the exponential. So now you need to have 15 more p's. You have b tilde to the sixth, which now gives you, of course, ppr to the sixth. Now it turns out the u's don't have just to give you p's. So you can get pw cubed. That's enough p's. And the last one can be an ordinary gauge field. If you look what's left over, you need r theta to the fifth now, just to absorb the 11 r's. So the expression you get now is d to the theta to the fifth, w cubed a. And that goes like d cubed, f to the fourth, which for the closed string translates into d to the sixth out of the fourth. OK, and again, the same group in 2013 computed this coefficient and, of course, also computed the indices. In this case, there is no RNS computation. RNS computation was only done for 4.2 loop and just would never short external states. This, of course, was done first in superspace. So you get not just the external graviton, but you get the whole supergravity multiplied, and the same in the three loop case. The coefficient was actually computed up to a factor of 3 in 2013. They didn't get the right answer according to the estuality conjecture, but they recently found a very simple error in the computation, and now they get the answer which agrees with the estuality conjecture. OK, so that's essentially a summary of what you can do with multi-loop amplitudes. So maybe in the last minute, let me just present some open questions. OK, so just to summarize, what we've done is shown how to obtain both the pure spinor and green Schwarz formalism from gauge fixing, a twisted like action. So this action here, surprisingly, the theta variables of green Schwarz come as for their pop-up ghosts. Now, there are many things one can try to do. So of course, one thing you can do is use the gauge-fixed action to compute multi-loop amplitudes. I think that's been done in such a convincing way that I think, of course, it's interesting to do it using other formalisms, but I think at least it seems to be clear that this is the simplest way to compute the multi-loop amplitudes. Now, there are other things one can study, for example, other gauge fixings. So it was shown how to get to the green Schwarz of pure spinor. But for example, can you get to RNS? Another question which was from the audience is there's some unitary gauge in which you don't even have fermions. Another possible use of this alternative gauge fixing is to maybe resolve this problem of the 1 over lambda lambda poles. So maybe in RNS, it's well known that you get these singularities, essentially, because your gauge fixing becomes singular. And it might be that there are other gauge fixings which resolve these 1 over lambda lambda bar poles. So this is, of course, a hope, but it doesn't sound so crazy. OK, another thing you can discuss is other backgrounds. So this, of course, was all done in a flat background. Of course, one thing you can do it you can't do in RNS is Ramon-Ramon backgrounds. In this case, it's a little bit strange, because it will turn out that the Ramon-Ramon field strings will only couple without derivatives, but they'll only couple directly after gauge fixing, because there's no Thetas, at least in the classical action. There's no way to couple directly in the classical action. They probably will couple through the BRST operator, but that needs to be worked out. Another thing that you can discuss is possibly non-critical strings. So using green shorts or pure spinner form is up to now. People have only discussed 10-dimensional supergravity backgrounds, just because we don't know how to describe any other backgrounds using green shorts, because you have Xs and Thetas. What else can you do? Of course, in RNS, there are many backgrounds you can describe which have nothing to do with 10-dimensional supergravity. You just have an n equals 1 will shoot super conformal field theory. So maybe this new kind of classical action will allow you to consider other kinds of backgrounds. So of course, that needs to be worked out. Of course, you can discuss other brains. So you don't have to discuss strings. So in fact, membrane, the d equals 11, super membrane of Berkshoff, Sezgen, and Townsend, can also be discussed in pure spinner language. Of course, they did in green shorts language. I don't know how to do it in RNS language, but it's also been done in this language. So that was in the reference that I mentioned earlier. And of course, there are other brains you could try to discuss using this new kind of classical action. OK, finally, there's the relation to twister strings. So this is a mystery, essentially, why these twister strings work. Up to now, I think the only explanation of why they work is because of, well, results that are being discussed by Freddie, these scattering equations. Somehow, scattering equations seem to fit in with. So twister string, it used to be the only string we had of this type was this twister string of Whitton and myself, in which you describe four-dimensional super Yang-Mills. Now, there are many other kinds of so-called twister strings. So one even has twister strings. I don't call them twister strings. They call them twister strings. They call them chiral strings, or infinite tension, which looks something like this action, in the sense that you just have p's and x's. You don't have a p squared term. And surprisingly, they describe the theory at alpha prime equals 0. So I don't know if anybody's going to talk about this here, but there are these nice results by Mason and Skinner, in which they essentially generalize these twister strings of super Yang-Mills to other kinds of string theories, essentially fitting in with the formulas that Freddie Koshas has discussed. OK, finally, unrelated to all of these things is ADS 5 times S5. So most of the computations that have been done up to now, using pure spinor formalism, are these multi-loop computations, essentially, because this is what Gomes and Mafra have been doing. But there's a whole other story, which is ADS 5 times S5. So of course, using RNS, we don't know how to describe this background. Using green shorts, you can describe it the classical level. And a lot has been done, for example, on Spectrum using classical green shorts and light cone gauge fixed green shorts. But to describe interactions, you really need something which is more conformally invariant.  And I suspect that it will fit very nicely in with this formalism. So some initial work has been done together with two ex-students, so Thiago Flurry and Tarlis Azevedo. So they have worked out together with myself, vertex operators, and started to compute scattering amplitudes. And this is, of course, another story, which is, of course, it's a different type of complication. But of course, it's very interesting, based on what other people are doing now. OK, so I'll stop there.


The Arab League has taken a significant stance for the first time since the Gaza crisis began, choosing to align itself with truth in the ongoing conflict. Its collective efforts are now directed towards opposing the occupation authorities and expediting the establishment of a sovereign Palestinian state. Recent actions documented by our teams include unilateral aid delivery, diplomatic advocacy for the Palestinian political system and outright condemnation of occupation actions. Particularly noteworthy in this update is the League's legal defence against the Israeli occupation of Palestine and its covert operations dating back to the 1940s aimed at thwarting the realisation of a Palestinian state. This marked a powerful moment in global discourse, characterised by a candid acknowledgement of truths and a firm denouncement of Israeli exceptionalism in the Middle East and Europe. Our commitment remains steadfast in delivering objective news and impartial geopolitical analysis. We urge you to engage with our content by liking and sharing this video to stay informed. Subscribe to receive timely updates on Palestine related developments. Palestinian people have been denied the exercise of their legal right to self-determination through the more than century-long, violent, colonial, racist effort to establish a nation state exclusively for the Jewish people in the land of Mandatory Palestine. When this began after the First World War, the Jewish population of that land was 11%. Forcibly implementing Zionism in this demographic context has necessarily involved the extermination or forced displacement of some of the non-Jewish Palestinian population, the exercise of domination over and subjugation, dispossession and immiseration of remaining non-Jewish Palestinians, the emigration to that land of Jewish people, regardless of any direct personal link, and the denial of Palestinian refugees the right to return, all operating through a racist distinction privileging Jewish people over non-Jewish Palestinian people. This has necessitated serious violations of all the fundamental Yos Kogan's and Urga Omne's norms of international law, the right of self-determination, the prohibitions on aggression, genocide, crimes against humanity, racial discrimination, apartheid and torture, and the core protections of IHL. Today I will address, first, violations of international law arising out of the regime of racial domination, apartheid, perpetrated against the Palestinian people across the entire land of historic Palestine. And then, second, the existential illegality of Israel's occupation of the Palestinian Gaza Strip and West Bank, including East Jerusalem, since 1967. As a necessary prerequisite, I must begin with this special right granted to the Palestinian people in the League Covenant. The legal rights of self-determination of the Palestinian people originates in the sacred trust obligations of Article 22 of the League Covenant, part of the Versailles Treaty. Palestine, an A-class mandate under British colonial rule, was, after the First World War, supposed to have its existence as an independent state provisionally recognised, a sui-generous right of self-determination. The UK and other members of the League Council attempted to bypass this, incorporating the 1917 Balfour Declaration commitment to establishing a national home for the Jewish people in Palestine into the instrument, stipulating how the mandate would operate. However, the Council had no legal power to bypass the Covenant in this way. It acted ultra-virus, and the relevant provisions were legally void. There was and is no legal basis in that mandate instrument for either a specifically Jewish state in Palestine or the UK's failure to discharge the sacred trust obligation to implement Palestinian self-determination. After the Second World War, a self-determination right applicable to colonial peoples generally crystallised in international law. For the Palestinian people, this essentially corresponded to and supplemented the pre-existing Covenant right regarding the same single territory. The 1947 proposal to partition Palestine was contrary to this, the Arab rejection and affirmation of the legal status quo. In 1948 then, Palestine was, legally, a single territory with a single population, enjoying a right of self-determination on a unitary basis. Despite this, a state of Israel specifically for Jewish people was proclaimed in 1948 by those controlling 78% more than three-quarters of Palestine, accompanied by the false displacement of a significant number of the non-Jewish Palestinian population, the Nakba catastrophe. This illegal secession was an egregious violation of Palestinian self-determination. Israel's statehood was recognised and Israel admitted as a UN member despite this illegality. Israel is not the legal continuation or successor of the mandate. This violation of Palestinian self-determination is ongoing and unresolved. Two key elements are, first, Palestinian people not displaced from the land proclaimed to be of Israel in 1948 and their descendants have been forced to live as citizens, presently they constitute 17.2%. Of a state conceived to be of and for another racial group, under the domination of that group, necessarily treated as second class because of their race. Second, Palestinian people displaced from that land and their descendants cannot return. These are serious breaches of the right of self-determination, the prohibitions of racial discrimination and apartheid, and the right of return. They must end immediately. As if this ongoing Nakba was not catastrophic enough, in 1967 Israel captured the remaining 22% of historic Palestine, the Gaza Strip and West Bank, including East Jerusalem, the Naxar. It's maintained that use of force to remain in control for the 57-year period since. For more than half a century then, a state defined to be of and for Jewish people exclusively has governed the entire land of historic Palestine and the Palestinian people there. And the regime of racial domination, apartheid, and denying return has been extended throughout. In the case of Palestinians living in the occupied territory, this has involved the same serious violations of international law supplemented by serious violations of norms applicable in occupied territory. Indeed, these people are subject to an even more extreme form of racist domination. What continues to perplex rational minds amidst the Israeli-Palestinian conflict is the world's silence in the face of blatant aggression by occupation forces in Palestine. It appears as though the world is held captive by the occupation, rendering it virtually impotent to respond decisively to the ongoing crisis which has stubbornly resisted any viable resolution. The existence of the United Nations coupled with its persistent inability to foster lasting peace in the region is raising doubts about its efficacy. There is an inherent ailment afflicting the organization reminiscent of its predecessor, the League of Nations, which may lead to its dissolution if it continues to echo the sentiments of a toothless entity. The organization has failed to deliver enduring solutions to global crises, often offering half-baked measures that lack enforceability, allowing powerful nations or those with significant influence to manipulate and even flout its principles. This was evident in the cases of Iraq, Syria and Libya. While it purports to possess the means to address threats to world peace, it often remains inert, yielding to the dictates of powers like the West in shaping the so-called rule-based international order. Could the cries for adherence to this international order also reverberate across Palestine, compelling the occupation to abide by international law and peacefully end its colonialist grip on historic Palestine? The impassioned plea articulated by this spokesperson underscores a silent world's complicity in colonial aggression. It's a stark reminder that the specter of slavery which we thought had been eradicated persists in the occupation of Palestine. The illegality of the exercise of authority itself. The enduring Palestinian right of self-determination means that the Palestinian people and the state of Palestine, not Israel, are sovereign over the territory Israel captured in 67. For Israel, the land is extraterritorial and, given what I said about the mandate, territory over which it has no legal sovereign entitlement. Despite this, Israel has purported to annex East Jerusalem and taken various actions there and in the rest of the West Bank, constituting de Ure and de facto purported annexation, including implanting settlements. It is Israeli policy that Israel should be not only the exclusive authority over the entire land between the river and the sea, but also the exclusive sovereign authority there. This constitutes a complete repudiation of Palestinian self-determination as a legal right, since it empties the right entirely of any territorial content. Actualizing this through de facto and de Ure purported annexation is, first, a serious violation of Palestinian self-determination and, second, because it's enabled through the use of force, a violation of the prohibition on the purported acquisition of territory through the use of force in the law on the use of force, and so an aggression. Serious violations of further areas of law regulating the conduct of the occupation are also being perpetrated, notably the prohibitions on implanting settlements and altering, unless absolutely prevented, the legal, political, social and religious status quo. The occupation is therefore existentially illegal because of its use to actualize purported annexation. To end this serious illegality it must be terminated, Israel must renounce all sovereignty claims and all settlements must be removed immediately. However, this is not the only basis on which the occupation's existential legality must be addressed. We need to delve deeper into both the law of self-determination and the law on the use of force. Beginning with self-determination, this right, when applied to the Palestinian people in the territory Israel captured in 67, is a right to be entirely self-governing, free from Israeli domination. Consequently, the Palestinian people have a legal right to the immediate end of the occupation. And Israel has a correlative legal duty to immediately terminate the occupation. This right exists and operates simply and exclusively because the Palestinian people are entitled to it. It does not depend on others agreeing to its realization. It is a right. It is a repudiation of trusteeship whereby colonial peoples were ostensibly to be granted freedom only if and when they were deemed ready because of their stage of development determined by the racist standard of civilization. The anti-colonial self-determination rule replaced this with a right based on the automatic immediate entitlement of all people to freedom without preconditions. In the words of General Assembly 1514, inadequacy of preparedness should never serve as a pretext for delaying independence. Some suggest that the Palestinian people were offered and rejected deals that could have ended the occupation, and therefore Israel can maintain it pending a settlement. Even assuming, arguing the veracity of this account, the deals involved a further loss of the sovereign territory of the Palestinian people. Israel cannot lawfully demand concessions on Palestinian rights as the price for ending its impediment to Palestinian freedom. This would mean Israel using force to coerce the Palestinian people to give up some of their peremptory legal rights, illegal in the law on the use of force, and necessarily voiding the relevant terms of any agreement reached. The Palestinian people are legally entitled to reject a further loss of land over which they have an exclusive legal peremptory right. Any such rejection makes no difference to Israel's immediate legal obligation to end the occupation. Turning to the law on the use of force, Israel's control over the Palestinian territory since 67 as a military occupation is an ongoing use of force. As such, its existential legality is determined by the law on the use of force as a general matter beyond the specific issue of annexation. Israel captured the Gaza Strip and West Bank from Egypt and Jordan in the war it launched against them and Syria. It claimed to be acting in self-defense, anticipating a non-immediately imminent attack. The war was over after six days. Peace treaties between Israel and Egypt and Jordan were subsequently adopted. Despite this, Israel maintained control of the territory, continuing the use of force enabling its capture. Israel's 67 war was illegal in the Yossad Bellum. Even assuming, arguing its claim of a feared attack, states can't lawfully use force in non-immediately imminent anticipatory self-defense. Alternatively, assuming again arguing that the war was lawful, the justification ended after six days. However, the Yossad Bellum requirements continued to apply to the occupation as itself a continuing use of force. In 1967, with self-determination well established in international law, states could not lawfully use force to retain control over a self-determination unit captured in war unless the legal test, justifying the initial use of force, also justified on the same basis the use of force in retaining control. Moreover, this justification would need to continue not only in the immediate aftermath, but for more than half a century. Manifestly, this legal test has not been met. Israel's exercise of control over the Gaza Strip and West Bank, through the use of force, has been illegal in the Yossad Bellum since the capture of the territory. The addition of this comprehensive legal context is highly valuable, shedding light on the deliberate erasure of history in the struggle for the soul of the Palestinian state. The occupying state has employed various tactics, including the manipulation of scriptures to assert direct ownership of the land of historic Palestine while undermining the laws of modern governance which should rightfully take precedence over any historical narratives. If every nation and tongue were to lay claim to the lands of their forefathers, chaos would ensue. The fact that indigenous peoples were already inhabiting the land of Palestine before the arrival of European migrants serves as a clear indication that the land belongs to a specific people and the rights of these indigenous people must be respected. We are deeply impressed by the compelling case made by this lawyer for an end to the occupation in Palestine. This is a narrative that the world can never forget. Israel cannot lawfully use force to control the Palestinian territory for security purposes, pending an agreement providing security guarantees. States can only lawfully use force outside their borders in extremely narrow circumstances. Beyond that, they must address security concerns non-forcibly. The USA, UK and Zambia suggested here that there is a sui generis applicable legal framework, an Israeli-Palestinian lex specialis. This somehow supersedes the rules of international law determining whether the occupation is existentially lawful. Instead, we have a new rule, justifying the occupation until there is a peace agreement meeting Israeli security needs. This is the law as these states would like it to be, not the law as it is. It has no basis in Resolution 242, Oslo or any other resolutions or agreements. Actually, you are being invited to do away with the very operation of some of the fundamental peremptory rules of international law itself. As a result, the matters these rules conceive as rights vested in the Palestinian people would be realized only if agreement is reached and only on the basis of such agreement. At best, if there is an agreement, this means one that need not be compatible with Palestinian peremptory legal rights, determined only by the acute power imbalance in Israel's favor. At worst, if there is no agreement, this means that the indefinite continuation of Israeli rule over the Palestinian people in the OPT on the basis of racist supremacy and acclaim to sovereignty would be lawful. This is an affront to the international rule of law, to the UN charter imperative to settle disputes in conformity with international law, and to your judicial function as guardians of the international legal system. A final potential basis sometimes invoked to justify continuing the occupation should be addressed. Occupation and human rights law, applicable to illegal and lawful occupations alike, oblige Israel to address security threats in occupied territory. However, they only regulate the conduct of an occupation when it exists. They don't also provide a legal basis for that existence itself. Existential legality is determined by the law of self-determination and the Yos-Ad-Bellum only. There is no backdoor legal basis for Israel to maintain the occupation through the imperatives of occupation and human rights law. In some, the occupation of the Palestinian Gaza Strip and West Bank, including East Jerusalem, is existentially illegal on two mutually reinforcing bases. First, the law on the use of force. Here the occupation is illegal, both as a use of force without valid justification, and because it's enabling an illegal purported annexation. As such, it is an aggression. Second, the law of self-determination. Here it's illegal again because of the association with illegal purported annexation, and also more generally because it is quite simply an exercise of authority over the Palestinian people that by its very nature violates their right to freedom. This multifaceted existential illegality involving serious violations of peremptory norms has two key consequences. First, the occupation must end. Israel must renounce its claim to sovereignty over the Palestinian territory. All settlers must be removed immediately. This is required to end the illegality, to discharge the positive obligation to enable immediate Palestinian self-administration, and because Israel lacks any legal entitlement to exercise authority. Second, in the absence of the occupation ending, necessarily everything Israel does in the Palestinian territory lacks a valid international legal basis, and is therefore, subject to the Namibia exception, invalid. Not only those things violating the law regulating the conduct of the occupation. Those norms entitle and require Israel to do certain things, but this doesn't alter the more fundamental position from the law on the use of force and self-determination, that Israel lacks any valid authority to do anything, and whatever it does is illegal, even if compliant with, or pursuant to, the conduct regulatory rules. I will close by quoting Palestinian academic and poet Rafat Alariyah from his final poem posted 36 days before he was killed by Israel in Gaza on the 6th of December 2023. If I must die, you must live to tell my story. If I must die, let it bring hope. Let it be a story. There is perhaps no stronger argument than to make the West understand that its tacit support for the ongoing war against Palestinians has tarnished its democratic reputation as a global exemplar. Each day that Palestinians remain without a state of their own, enduring constant bombardment by the occupation, exposes the true nature of an empire built on deceit and subterfuge. It is an empire that espouses equality and human rights only when its own interests are at stake, a hypocritical stance that has been laid bare before the international community. Just as it boldly condemns the brutality of the Russian invasion of Ukraine, a peaceful democracy in Europe, it should also have the courage to denounce the arrogance of the occupation in Palestine, and demand a more civilized approach that allows Palestine to attain freedom. Indeed, this presentation stands out as exemplary and warrants sharing. Thank you for your attention. Please consider sharing and liking this news update with your loved ones. Don't forget to subscribe for the latest developments from Palestine. Until our next update, peace.


Welcome to the Core Report. I'm Corporal Remington Hall. And I'm Corporal Kathy Nunez. After 72 years, First Lieutenant Alexander Sandy Bonhamon Jr. is finally home. He was among the 36 unidentified Marines recovered from tarot earlier this year. In case you didn't know, Lieutenant Bonhamon was a badass. He was posthumously awarded the Medal of Honor for leading an attack, which included crawling more than 40 yards to capture a Japanese bunker and flushing more than 100 enemies into the open where they were eliminated. He was mortally wounded during the attack, but the U.S. secured the island the day he died. Lieutenant Bonhamon was laid to rest in his hometown of Knoxville, Tennessee, Sunday. Semper Fidelis, and welcome home, sir. For the full story and his Medal of Honor citation, click the link in the video description. Last week, General Robert Kneller officially relieved General Joseph Dunford as commandant of the Marine Corps. General Kneller's first actions as commandant was to publish a letter to the Corps. In his letter, he states that he will release an augment to the current commandant's planning guidance by the new year. To read General Kneller's full letter, follow the link in the video description. The next day, General Dunford clocked back in to relieve General Martin Dempsey as chairman of the Joint Chiefs of Staff, making him the highest-ranking military officer in the United States Armed Forces. This is only the second time a Marine has held the position. When a 7.0 magnitude earthquake hit Haiti in 2010, Marines were there to lend a helping hand. Marines have returned to Haiti every year since. Operation Continuing Promise is an effort to continue to help the people of Haiti. As part of the disaster response, Marines have conducted civil assistance, medical, dental, and veterinary aid, and engineering support. Operation Continuing Promise doesn't stop there. Marines with the operation travel around South America, Central America, and the Caribbean, providing humanitarian aid to different communities. For more information on Continuing Promise, see the link in the video description. Remember, you can catch up on everything else going on around the Corps by logging on to our official social media sites. Thanks for watching, everyone, and we'll see you next payday... Right here on the Corps Report.


in today's video we're opening a first edition ancient sanctuary vintage yugioh box okay first edition ancient sanctuary hobby box is being open today inside we could pull enemy controller first edition we could pull burst stream of destruction we could pull dark magic attack arch lord zirato cover card i mean as you can see behind yugioh there i mean they're covering up his face a little bit but the wings very awesome their secret rare miss ira de vil we're hoping that we get that today let's crack open this box here we go first edition cutting it open oh there it goes everybody enemy controller a box or not enemy controller ancient sanctuary this was my first old school box opening back in 20 early 2019 i believe could have even been 2018 but i'm pretty sure it was 29 yeah it was definitely 2019 so it's always a little nostalgic for me to open this up we have first edition here here we go open this thing up only 24 packs in this box we've been doing a lot of 36 pack box breaks recently but there was no 36 pack we're ancient sanctuary they stopped that in dark crisis so ancient sanctuary back to all 24 pack boxes there's also retail 24 pack but this should be a hobby box and that means it's the exact same as retail except except it has a different secret that's it for the originals okay we are shuffled up everybody our first person up is tim h with four packs all right tim four pack magic here want to get him something good let's see what we can get there will be no rucksons specials today i'm declaring it now will we get first pack magic like we did in the magic ruler box break i don't know we have protector of the sanctuary mermaid knight ninjitsu art of transformation arcane archer of the forest wide magician peekaroo sole reversal as one apparition judgment of the desert and a thousand energy what does that even mean thousand energy like is energy a unit that you can say thousand like i don't even understand that card i don't even remember that card hope you guys are enjoying the video because we have a giveaway i'll be giving away these three goat format cards got them right on my goat format box just like the video be subscribed turn notifications let me know down below your favorite card from ancient sanctuary i should have given away a knight assailant now that i think about it i don't know that'd be pretty cool oh well i guess don zulu will have to do ancient sanctuary pack number two four tim will this be our first foil we're expecting on average two ultras four supers maybe a secret we have arcane archer could be some variants there that's that's standard dust barrier sonic jammer rucksons special dang it second pack already messed it up desert sunlight all right judgment of the desert absorbing kit from the sky goblin thief 2 000 needles and an amplifier genzo let's go genzo time not quite the full genzo but we do have the power of the amplifier super rare very nice we got an overunder all the rucksons specials in the chat everybody you gotta believe in me it's gonna be under it's gonna be under we've got some threes in the chat will there be three rucksons specials not sure okay third pack for tim it's got one foil so far it's not bad it's a decent start the 3.5 has been set if you are watching on youtube video or if you're in the live stream will it be over will it be under three and a half rucksons specials i've already gotten one so i'm giving i'm gifting you on there mystical shine ball i'm going under delta attacker fiend scorpion which is also on the delta attacker card pretty interesting we have labyrinth of nightmare going back to those old school cards perot army human wave tactics solar flare dragon the law of the normal and the thema nightmare who always makes an appearance in ancient sanctuary it's impossible to avoid one two three four we have delta attacker elephant statue of disaster fiend scorpion labyrinth of nightmare human wave tactics atomic firefly solar flare dragon the law of the normal and we have soul absorbing boned hour okay one out of four not terrible tim but also i'm sure you're looking for a little bit more probably but hey at least you got one of the best supers in the set amplifier is definitely one of those i will be double sleeping this after the stream but i'll get this in a top loader for you right now all right next up okay we have hector r with four packs hector good luck one two three four here we go four more packs so far one super has been pulled let's see if we can turn that around get an ultra or a secret oh man there we go that that's better okay that one didn't rip well one two three four what will we get four hector we have dora the explorer fate mystical shine ball delta attacker elephant statue of disaster man throw trove with the old drama yellow hey buddy metal armored bow solar ray goblin king the agent of force marz okay i thought there was one more card another hollow agent of force marz is it hollow wait what am i supposed to say i say foil or hollow is it which one do people prefer because like some people get mad at the other one i don't remember which one it is agent of force marz super you can say super that's probably what they want okay good start hector you already got a super room one two three four okay fiend scorpion labyrinth of nightmare regenerating mummy weapon change goblin king mystic walk emissary of the oasis micro ray and double cost in okay attribute that dark magician hector's one for two what's he getting in his third pack of ancient sanctuary seventh pack overall we have two super so far no ultras no secrets seventh pack burst dream of destruction here it comes here it comes guys one two three four will it happen wall of revealing light rocket jumper monster gate night of sale those are too good to commons in a row we have piranha army human wave tactics solar flare dragon law of the normal and the talisman of spell ceiling all right one for three as well very similar to what uh we did on the first four with tim all right here we go last pack four hector will he get another foil monster gate at it again night of sale and another man some good comments here dora hector shineball mystical shineball hector's mystical shineball back fire we have lakuta earthquake piranha army and we have a first sarcophagus another super interesting so it's all super rare is right now so three supers no ultras no secret not bad for hector two for four is pretty good very very good four packs we have eight packs in now out of 24 we're a third of the way through the box no ultra no secrets hopefully we don't get another one ultra box like we did in the one not one that was rough who's up next it is michael s back at it again with five packs so he's going to get us all the way through to the next half so four on the right side then the fifth michael s good luck um these do not want to open they rip weird yeah these are these are so bad at ripping okay we got it out though so that's good okay one two three four ninth pack sonic jammer we have desert sunlight spirit collar blessings of the nile soul reversal as one apparition armor break judgment of the desert and seal master me say okay another rare four packs left first edition ancient sanctuary what can we do it'd be nice to get a uh as a borg as well that'd be cool one two three four i've not pulled that yet we have legendary jiu-jitsu master another nice card beckoning light another nice card mochi mochi actually worth a couple bucks short print i think vampire lady absorbing kit from the sky goblin thief two thousand needles order to smash and the agent of creation venus guess who just asked for venus luna there you go there's another venus or a venus not another three packs michael s is o for two let's get him something good one two three four we have protector of the sanctuary order to charge mermaid knight nijitsu art of transformation the unhappy girl disc fighter soul reversal and finally not finally as one apparition and special hurricane that's a rare o for three for michael two more packs come on blowback dragons in years well there are a lot of decent cards in here actually that you kind of look not a normal hurricane for sure one two three four gigabyte it's going to need more of that for our storage monster gate rucksus special anitis salin that's a lot of those and that's a play set of those in this box already door of fate backfire lakuta earthquake pharaoh servant wow we're going to be opening speaking of pharaoh servant pharaoh servant first edition will be the next box break we're halfway sold out go check it out on my website rucksons34.com if you are a member of special footage or greater you get ten dollars off per pack and finally grave protector all right that is four in a row for michael come on michael last pack magic form this is the first pack on the left side come on michael we have a fiend scorpion labyrinth of nightmare regenerating mummy interesting that they got pharaoh servant and labyrinth of nightmare in the same light set as cards weapon change we have mystic walk emissary of the oasis micro ray disc fighter and oh avatar of the pot this is the guy I was trying to remember from the pot collection I was like there's who's that weird pot guy this should have been in the pot collection should this have not been the in the pot collection imagine having a little figure of this guy it'd be awesome speaking up go check out our pot collection video if you missed it but all right michael that was a rough go for you I think you did pretty well last time so it's kind of balanced out but this is you know you did good on a better one probably last time but michael s you'll be getting bonus foils of course send you something to make up for that next we have Josiah be with six packs so as I said not a lot of oh there is there is a couple one pack magics coming up they're going to be on the last few packs three four five six so six packs that leaves us with only yeah that's right okay five packs after this Josiah be here we go guys one two there's another mystic walk look at that there's a mermaid knight come on Josiah new jitsu arc arcane dust barrier that was a rucksack special mystic walk oh there's a three dollar card so yeah there's another rucksack special emissary micro ray disc fighter and oh we've got a ghost night of jackal our first ultra rare there it is not one of the ones we're probably looking for still though it is a pretty amazing artwork look at that that is super cool ghost night of jackal Josiah great start you've already gotten one next pack one two three four we have a generating mummy weapon change mermaid knight and jitsu art of transformation metal armored bug solar ray goblin king mystic walk again we're in all the good comments and the agent of wisdom mercury more agents have been pulled four left for Josiah first edition here we go can we get that econ burst dream of destruction dark magic attack arch lord zirato secret rare of any kind 14 likes away from 200 likes you guys remember what that is guaranteed amazing pull according to you know just the whisperings around the opening enchanted fitting room we have sand gamut walverville like the band or formerly limited card rocket jumper kick man hit manly go giga giga solely to get some different commons this time and spell economics who's taking economics okay three packs left eight likes away from 200 the lucky number oh look how this is opening there's like nothing to pull what in the world is happening here and have to open this like backwards okay that was weird these do not want to open today these do not want to open today all right that might be enough there we go got it out all right one two three four Josiah and one for three let's see if you can get another dust barrier sonic jammer desert sunlight pharaonic protector maybe that's what we were thinking of pharaonic guardian absorbing kit from the sky goblin thief 2000 needles seven the longest name in yugioh and soul resurrection and back at it again come on it's just not going to open up these are not going to open up correctly for us today order to smash one two three four the order to smash has been given spirit caller we have blessings of the nile legendary jujitsu master back in light we have order to smash again but not really it's the same card the kick man hit manly we have soul eater new bean guard and the king of the swamp rare pretty popular with tear limits there for a little bit final pack for joe size one for five can you go two for six here we have one ultra three supers no secret yet still looking for that secret let's go can we get a secret or an ultra here one two three four only five facts left after this enchanting fitting room with those ojamas sand gambler rocks and smash there's another one wall revealing light we have a rocket jumper order to smash the kick man hit manly sword of the soul leader not swordsman new bean guard and triangle power with the gigabyte on on the screen i love the gigabyte he's cute joe syah congrats on the ultra the first ultra of the box so all right next pack one pack magic joseph h good luck joseph one pack magic first of the day can you get an ultra or a secret let's do this oh one two three five didn't drop the cards like you thought i might i almost did mochi mochi nice common vampire lady enchanted fitting room the sand gambler backfire second sarcophagus i believe is a short print three on plakuta earthquake come on baby talisman of trap sealing no one pack magic for joseph today that leaves us with four packs left in the opening okay one pack magic again our last one pack magic for jared p good luck trying to open this without ripping it too bad if it worked one two three four can we get another foil night assailant door of fate we've gotten like four or five night assailants have been really good mystical shine ball we have delta attacker law the normal we need an ultra or a secret we're probably gonna get another super too object camouflage we have metal armored bug solar ray and the secret rare end of anubis i thought this was a missera box maybe i'm wrong i always get these two confused we have a secret all right end of anubis very nice it looks like it's in great condition too which i haven't been doing to that guy who was mad that i was looking at the point that's actually really nice has the sin ring it's a little bit off to the right okay hobby boxes anubis okay i was wrong so did we open a retail box for what not then didn't we maybe i mixed them up and did the did it backwards oh well okay we got secrets of both of them so that's good okay that's sweet end of anubis is really cool didn't even do this get expensive for a while for like some deck or something very nice i always get that would get used apparently but one pack magic jarrett wow dude that's insane secret rare has been pulled so we have officially one secret one ultra three supers with three packs left and we still have one guy left omar r which i actually just recorded an opening for omar you guys are gonna see soon three pack magic should be at least one foil hopefully two hopefully we'll get a second or a second ultra and then a second super and not have another one ultra box let's do this one two three four are we gonna get something we have regenerating mummy weapon change protector the sanctuary order to charge metal armored bugs solar ray warrior of zara goblin king training shield all it's gonna come down to the last two ah come on get it all we just want an ultra we didn't care about the super just get an ultra look at these these do not want to rip there we go we got it okay one two three four come on blessings of the night with legendary jiu-jitsu master beckoning light vampire lady absorbing kit from the sky second to last pack magic goblin thief 2000 needles seven longest name in yugioh and the oh it's a six pack box please don't be a one ultra box again ancient what's up with ancient sanctuary being one ultra boxes please don't do it again be an ultra just be a three super box that's all we care about last pack magic come on send the luck in the comments omar one two three four i believe wall revealing light last pack magic come on rocket jumper gigabyte we need an ultra rare econ dark magic attack or burst dream infrastructure we have monster game earthquake piranha army human wave tactics oh is it the next one or is it one more it's one more after that solar flare dragon here we go last pack magic here we go no it's a super ultra box oh at least we got the secret i guess i don't know i guess you'd prefer the secret one ultra but it still sucks when you lose an ultra all right so six foil box we didn't get the seven like we're hoping ah still at least you got some emissary last pack magic emissary is good for exodia they're gonna play that okay a little bit of a disappointing ending but overall a decent box we did get the secret and pretty good supers the ultra you know one ultra not a great ultra so that's kind of a rough ending but it was still fun if you guys enjoyed it don't forget to subscribe to the channel and i will see you guys in the next one peace shout out to the home photo puffins of doom or nested dn america doid steward brad kk beats and then a tie show ian musa junior barding robert f thomas beclaim changeling and joey castle thank you guys for supporting the channel and i'll see you guys next time peace