 Okay let's start. Good afternoon to all of you. So as you will know Joe Polchinski passed away last year. It was a very sad moment for all of us who knew him. It's a moment for all everybody who was interested in physics on the deepest level. So last year during the spring school we decided that talking with Attish and Narain that it would be good to first of all to have a discussion there at some some some words in honor of Joe at that time when we were here we asked Igor Klevanov who was one of the lecturers to say something but we decided to start from this year on a colloquium name after Joe to honor him because of all these contributions that he had made to theoretical physics in particular to string theory. We claim that this activity the spring school and spring theory at ICTP is the longest-running activity in string theory so we will be very honored to have for every year and this activity a colloquium, a special colloquium in honor of Joe to remember all his contributions to our field. So many things have been said about Joe during the last year. There are very beautiful and emotional articles that you can find in online. There was a special event in his honor on the 15th of December last year and with some a lot of physics but a lot of interesting anecdotes and emotional comments by many people who knew him, who loved him. He has touched so many lives. I personally felt very thankful to everything he did for me since I was a student and he held me throughout my career. Also for ICTP he was always a regular lecturer here and then he was a Dirac medalist and he was a member of the panel to select the Dirac medal until he asked us to replace because he couldn't continue due to his health issues. Actually here is one of the anecdotes of his careers that happened actually in this room. If you all know Joe, when he was given an answer to a question and he had to concentrate, he would close his eyes and start talking about it with all these ideas in his mind and the joke is that apparently in one of these opportunities he had to wake him up. Narain here was a witness of that, so he said Narain, yes. There are many things that people have said about Joe and we will miss him very much. His contributions to the field were tremendous, deep thinking about the string theory, introducing deep brains in general, but also contributions and effective using for surface and with Sony and realization group approach and issues about the cosmological constant, lots of information and black holes and so on. So his legacies is huge and we owe him a lot and we miss him a lot. So it's important to have something to remember Joe and so for this opportunity we finally found someone who will fit very well to be the first speaker for this special lecture on Joe. Paul Townsend has kindly agreed to be the first speaker for this colloquia, the series of colloquia and it feels very well because Paul as you know is one of the persons who initiated all the study of super main brains in general, P-brains. Actually he invented the name P-brain in the same way that Joe invented the name D-brain and there are several stories about that. Actually some of them also happened here when he came and did his research with the local people, so you will say some of this in your talk. So and then he later on he was a key person of what people call the second string revolution, a paper with Chris Holt. It made everybody clear at some point there would be this duality that uniting all the different string theories and in particular with the contact with the 11 dimensions and main brains and Paul has been a major figure for that. So I think Paul is the ideal person to give these lectures. Let me say a bit more about Paul. In the early 80s he came to Austin when I was a young student, so he helped me also to in my thesis, so I was very thankful to Paul and many years later we joined, I joined Cambridge and so he was a lecturer, professor there, so we had many many experiences together and I have been pleased by having this opportunity to have to share a lot of time with Paul. There is an anecdote also with the four main characters Paul, me, the Queen of England and her husband. I will not tell you the story because I'm the bad guy and Paul is a good guy, so if anybody's curious they just come and ask me later on because I would be embarrassed to say it in public, but it's true. So anyway, so it's a pleasure to have Paul here and please join me to welcome Paul Townsend for this colloquium. Good, it's on, yes. Ah, I was wondering what that story was. I, me, you, the King and Queen of England or the Queen and consort or whatever. Yes, I remember now, but it's a bit too long and not relevant, so on some other occasion. Yes, it's a great pleasure to be back here because about 30 years ago I think I was standing in this room delivering a talk called Peabrains for Peabrains and afterwards the organizer, my colleague and friend, Erkin Seskin, was very angry and came up to me. How can you do that? And he would not let me use that title for that my contribution to proceedings, so he changed it. And in fact, not long after that, I think the first time that I tried to use a similar title in, in a journal, it was rejected by the referee said that I was bringing the field of physics into disrepute. But so how times change? It's nice to be back here. It's nice to be back here because that's, I have memories associated with the topic of this talk, Tonight Brains. And also because Joe Polchinski's work had a tremendous impact on my work in that subject as well as having, of course, tremendous impact on other people in that subject and on lots of other topics. I should say to begin with, of course, I'm not going to cover all of Joe, all of everything that Joe did in his career tonight. I'm hoping that in the future years, as we've just heard, there will be other people to come along. So I'm focusing on a few things where in the context of Brains and where he made an impact and in particular where he made an impact on me. So there's a subtitle to this is What I Learned from Joe Polchinski. I should say that prior to the, so about 30 years ago I was here, but sometime before that, in fact, it was in 1983, but Fernando mentioned, I went to Texas for six months. I went there only for six months. Initially it was going to be longer, but I, after I had agreed to go to, to Austin, I got a phone call offering me the job in Cambridge, which I had to accept, but obviously it was a permanent job. And, but I, I, you know, I persuaded them to allow me six months in, in Austin because I had sort of already committed myself. So I was very pleased to go there and I met, it was just before Joe Polchinski arrived there. So all when it really, when I arrived, I was hearing about him because at some point soon we knew that he would be coming I think the following year. But since I was only there six months, in fact, I never, I never met him there. But I did meet two other people there who, who did get to know on whom Joe had a tremendous impact. And one of them is Fernando, as Fernando pointed out. He was, Fernando was taken on by Stephen Weinberg as a beginning graduate student. And in fact, Weinberg asked me to give Fernando a problem on supergravity. We were just discussing that problem the other day over lunch here. And also it was Luca Mesonchesco was there, who I wrote some papers with while I collaborated there at the time. And I've been working with him on things, on and off ever since. And those two people will actually appear at some point in this brief history of brains. And it's appropriate because Joe's, Joe's death was a loss. At least for them, particularly it was a personal loss, as I know he made a big impact on them. As well as the loss from physics. For myself, I actually met Joe only, I think in the late 1990s, probably in Santa Barbara, but that was the first time. And then I remember later on in Cambridge, the Cambridge University bookstore. That was the time when I was promoting the idea that we should stop these conferences on strings and start calling them brains. Brain theory, 2000. 2001 brains was the idea. And he said, but Paul, you know, is it really against string theory or is it just a persona? And I said, Joe, how can I be against strings? Strings are one brains. Well, so I'm, I've called this a brief history of brains. And of course, it's brief in various aspects. It's not going to include, it's only going to go up to a certain time. And it's also not going to include all kinds of sort of things on the side. So I take a kind of one-dimensional slice through that's essentially determined by largely, well, to a large extent, by what Joe did in this, in this field. And, but since it is a brief history, of course, I have to start at the beginning. And that starts with, that starts, here we are, with Dirac in 1962. And so he introduced, Dirac was always interested in, he didn't like renormalization theory, that was the point. And he tried, he thought, he had the idea, he thought that you should solve the self-energy problem classically before you start to do it quantum mechanically. In fact, the fact that he didn't like renormalization theory, I think was actually rather a good taste, because people, renormalization really wasn't understood properly until mid-70s. He was still alive then, but very old. And so I think his, his objections were, were probably rather sound, at least at the time. So he wanted to have, he wanted to go back to the electron and have some kind of extended electron model. But he wanted to do it relativistically. You know, people had tried at the beginning of the century, Lawrence and others. He wanted to do it relativistic. So, so he introduced this relativistic membrane in which the, the action is simply the, is simply the, the volume of the world volume. So you have a two, two-dimensional surface. It moves in a four-dimensional space. So there's some three-dimensional hypersurface. And induced on that hypersurface is some metric. You get some natural induced metric, metric from the Minkowski metric in space-time. And you just work out the volume, put the tension in front of it, to get the right dimensions, put a minus sign so that the energy is positive. And that's the action that, that Dirac wrote down. And his idea was to make it spherical, had a spherical membrane. And it's going to divide, that means it's going to divide into an interior and exterior. And his idea was that you have electromagnetic fields only on the exterior because you put conducting boundary conditions. So there's nothing in the inside. The electric magnetic fields are all on the outside. And so basically this was, this, this was, this was his model. I have a pointer here, don't I? So, so this was his model. And his idea was to basically he looked at the ground state and he fixed that energy to the electron and then he wanted to look at the fluctuations. So the first excited state he tried to identify with a muon. It's a very basic model because it doesn't include spin, for example. But nevertheless, it was the first, it had repercussions later on. There's a very similar model which I'll, I'll mention later. So moving on to the, to the beginning of the 70s, of course, from the dual models, we have the, the idea that it's a string and Nambu is associated with that. And he came up with Nambu-Goto string. I've never seen the paper by Goto. So I'm not, not sure exactly what was done there. But three, a few years later, Nielsen and Olson realized that that you should also, you could also interpret that action as an effective action for some kind of string like soliton solution. In fact, they picked the vortex. So if you take the Abelian Higgs model in three dimensions, that has a, so two space dimensions, there's a vortex solution. And if you just add a dimension, it becomes a string. And they had the idea that, that this, this action would be the effective action at low, low energies for this vortex string. And that's, that particular interpretation is going to play a significant role in what I say later, because that was taken up by, by Joe in the context of supersymmetry. So there's this interpretation as a fundamental string, but there's also an interpretation as an effective action. And the question is, how do we incorporate supersymmetry? Okay, well, I will try to use the blackboard because I'd like, try to stick to the, the, the scheme I, I have, I have in front of me rather than on the, the page there. So the point is that some, so if we come to the idea is that P-brains couple, I'll be schematic here to P plus one form potentials. And so that's, it's basically a generalization of the Lawrence force law for particles. And so first of all, you have a calbin, so on 76, we have Calbremond. And they had the idea that you have just as particles will interact through an intermediate electromagnetic potential, they had strings interacting through an immediate intermediate two form potential. So in that case, they had a coupling, which was an analog, so just an analog of some two form, generalizing the coupling. So that's some kind of string charge. And then there's a natural generalization of that to, to any number of forms. And that was considered in already in 77. And this is a particular model that I wanted to. So it's a really a Christodulo, I won't bother writing down the names actually, just to save time. It's a character Antonio Aurelia, who I'll mention later on. And they had a model, which was the following. They said an interaction, they was like the Dirac one, where they had their membrane action. But now the point is that there's a natural coupling of that membrane to a three form. So this is, so they had an extra term in here, a, and this is some three form potential. Whereas Dirac sort of put conducting boundary conditions, it was a little bit ad hoc. The natural interaction of a membrane is really with a three form. And so they were really realizing that in an explicit model. And then essentially they took, again, in four dimensions, they had this membrane having you have an inside and an outside. And then they only had this integrated over the outside. So this was a, and we had some now four form field strength D of a three. That was their model. And it was a kind of, this was a kind of bag model. So this was a kind of bag model. And this was really, this was in 19, well, this was in 1970, 1977. But Antonio Aurelia came, I was at CERN in 1980, and he came to my office and he told me about this model. And that was my first introduction to the relativistic membrane. And in fact, we worked on this in relation to 11 dimensional supergravity. We had an article we wrote on 11 dimensional supergravity. We'd use the fact that there's a three form in 11 dimensional supergravity. And so that was the first time that I had the, that was the first time, well, that I saw it together, 11 dimensional supergravity, a three form I learned from these people that if you see a P form, then you should realize you should couple that. So if you see a P form, you should be looking for a corresponding brain. And if you see a brain, you should be looking for a corresponding three form. So that was a point that stuck with me at the time. But another reason I want to, I mentioned this model is because it was taken up, because eventually it's a trail that leads to, to work of Joe. Because this was taken up. This model was realized that, that by Brown and title boy. And that was in 1986. And so they had the idea of a nucleation, nucleation of membranes. Now, I should first of all say, of course, that that there's this context here in which this model appeared as a bag model. But you the idea was that in fact, when Antonio really came to tell me this, I was working about his model, I was working on supergravity. And I was interested in the fields and supergravity. And it was obvious that you should, you should try to interpret this in a gravitational context. And in that context, their interior of their bag, where they had this F4 not equal to zero, that that would be a cosmological constant in the, would be a cosmological constant in the context of gravity. And indeed, what happens is that so you have, there's a connection between membranes and the cosmological constant. So the point is that if, let me just write down, I'm going to try to be very schematic here. So if we have, if we couple this three form to gravity and not just to something else, forget about the membrane for the moment. And just look at the three form itself. You see that the equation is for four is equal to this. So that tells you that you have F4 as a constant. And that's an integration constant. So that integration constant, if you put it back into here, call it M. So you end up with a cosmological constant, lambda, which is strictly positive. So the idea was that instead of having this bag model, you would have a cosmological constant inside. And Brown and Tithable suggested that they realized that, oh, oh, thank you. Yes, that, that would, that would help because maybe I'll let you keep going on that for a moment. I just, they realized that if you have an inside, so take the inside and you have, if you have F, which is small, and on the other hand outside, you have F, which is large, then if you expand this, you're going to decrease the energy. And that's a volume effect. On the other hand, to expand it, you have to, you need energy because you have the tension of the membrane, which is a surface effect. And so you initially need energy, but you get it back at some later stage. And so there's a kind of, there's a, essentially, a barrier to the production of membranes, but you can tunnel through that. It's a little bit like the, it's essentially the Schringer pair production process for charges in a constant electromagnetic field. So the exact analog of that will produce these membrane bubbles. And their idea was that you could use that as a way of taking, starting with a large cosmological constant, and eventually these membranes would nucleate and you'd end up with a small cosmological constant. Now, that didn't, what, if you compute the rate as they did, you discover that in fact the rate becomes, is, becomes too long. So phenomenologically it wasn't interesting, until Joe came along in 2000, with Raphael Busso in 2004. And he pointed out that this, this four-form field strength in the interior, or the exterior should be quantized. And that's reasonable because if there's some basic membrane, then across it you should expect some discontinuous, particular discontinuous change of the four-form, of the, basically the cosmological constant in the inside from the outside. And then you have a situation where as these membranes nucleate, you sort of populate some multiverse with large numbers of bubbles in which you get different values of the cosmological constant. And if you, if you combine that with the ideas of Stephen Weinberg on the anthropic selection principle, then you basically get an explanation for why the cosmological constant is small today. Initially, of course, at the time that Brown, Brown and Tidal were around, everybody thought the cosmological constant was zero. And so they were trying to get zero, they realized they couldn't get zero. And that's why, because the rate became too slow. And that's why their model was forgotten for many years. But when we discovered that in fact it's just small and not zero, it was resuscitated by Raphael Bousso and Joe Polchinski. Okay, so that's a little bit of a diversion, because what I want to come back to now, which is in fact the main thrust of the talk, is the, how you incorporate supersymmetry into the picture. So there is a natural coupling to, of brains to pre-brains and something I learned and took to heart in the early 80s. And then this connection with membranes and cosmological constant came up and was relevant to, Joe made very good use of that later in what I think is probably the best reason that we have the best explanation, possible explanation, I don't know if it's right, but it certainly seems to me as the best one we have for why the cosmological constant is zero. But as I said the main thrust of my talk really is to deal with the supersymmetry. And so the issue in fact, the issue is how do you introduce supersymmetry, well the truth is that maybe some people thought about that before Green and Schwartz, well in fact they did, because that topic was raised in the context initially of particle mechanics. So it was realized at some point that what you have to do is instead of having a particle moving in space you have to have it moving in super space because then basically all the symmetries of your super space, which includes supersymmetry, will then be symmetries of your particle action. But the question was how do you generalize that to the string? And one of the things that not too many people were looking at that because we're before 84, before the string revolution. But when Green and Schwartz came along and solved and did the anomaly cancellation etc. One of the things they did a little bit later was to write down an explicit action. And essentially there's in all of these things there's an obvious term which you write down because it's just the Dirac type term but it's it's essentially some metric that you induce instead of from ordinary space from super space. So that's the kind of standard thing that you think of. But if you just take that alone it's not going to work by itself. I can still use this as a pointer, right? So the first term isn't going to work by itself and so the real the idea was to come up with the other term and so that was that's what took the ingenuity of Green and Schwartz. And they realized that basically if you start with a three-form that's closed you can write it as a d of a b2 of a two-form but in the field equations only the three-form will appear. So as long as that three-form is invariant under all your supersymmetry transformations, superpointer, then you're okay and that will, action will have the right symmetries but that's by itself still is not enough. You have to choose the combination between them. Now you've got two terms and you have to choose the coefficient between them and they realize that they can choose this coefficient to have a particular so called kappa symmetry. And let's not go into the details of exactly why that's needed. You need it in order to get the right number of degrees of freedom etc. But that's that's an essential ingredient and for a particular choice of this constant they realized you could do it. And the point I want to address here is there's a parameter and the parameter is a self-dual worldsheet vector. And if you go and look in green schwarz and witten and you look at the particular chapter where they discuss this string you'll discover that indeed it's still written in that book as self-dual worldsheet vectors. So they had an opportunity to change it I think 25 years later on but they decided to stick with that. It's not wrong but as you'll see it's somewhat misleading. Now so that was the green and schwarz and let me just make a point of course and everything I said there the dimension didn't come into the game but there's a nice as green and schwarz realized there's only works and their construction only worked in particular dimensions. And what it requires is a particular Dirac matrix identity for it to work and you can you can a nice way to state what that identity is in terms of some commuting spinner. You have some commuting spinner and you have to construct another vector spinner from three of them. That's the left hand side and that has to be equal to zero. And if that identity holds then you can construct your string solution and as green and schwarz showed in fact that works only in three four six and ten dimensions. Of course ten dimensions was the case that they were mainly interested in but you do get the others as well. Now you'd say you know why would you get these dimensions? Well there's a nice explanation of that which was provided by Jonathan Evans he's in Cambridge a few years later and he noticed that he realized the this identity green and schwarz had is actually equivalent to an identity that had been proposed by the mathematician Adams way a few years previously it's kind of called a triality identity and it's an identity that's necessary if you have an algebra in some dimension for that algebra to be a division algebra it has to satisfy this triality identity of Adams. He pointed out that in fact this is exactly that identity just written in a different way. So this is the physicist version of the mathematician's triality identity and so you use you learn immediately of course that that's the transverse dimension d minus two so d minus two has to be one two four eight and so you get the d equals three four six and ten and you see they're associated then with the real complex complex numbers quaternions and octonions because those are the four division algebras and of course a nice thing here for what I'm going to say next is that there's a four-dimensional green schwarz super string in addition to the one that green and schwarz were interested in which is the essentially the octonionic version. Now I come back to this point about these vortex strings so the point is first of all so this is the issue is as follows that if you take one of these vortex vortices the idea is that you can consider them in a supersymmetric field theory too so for example in particular the abelian Higgs model is a supersymmetric extension of that abelian Higgs model and then you can ask yourself the question okay what's the effect of action now because now you're going to have an addition you're going to have additional fermionic variables on your well sheet so you now expect some kind of super string action what could it be well the first point to realize is that this vortex saturates this bogamol bogamol bound I think it's one of the ones that was originally in the original bogamol paper in terms of some topological charge and it was shown by witton and olive in 1978 these such cases the central charge appears as this topological charge appears as the central charge in the supersymmetry algebra and the net result of that is that the vortex preserves one half the supersymmetry so this is a classic example of what we now would now call a half BPS soliton now that's in the three-dimensional context it's a soliton if you go to four dimensions just add one direction you've got yourself a string and now you have and the nice thing there is that the you can add one more direction because the you can do the super symmetric abelian Higgs model in four dimensions not just three so if you do that then you get now four-dimensional supersymmetry and that's basically two two from respect with respect to a two-dimensional decomposition and that's broken to half of that in fact to zero so now there's nothing particularly surprising about the fact that the vortex string you know general configuration breaks everything this particular vortex string preserves some supersymmetry that means it's half preserved in half half broken but there's a puzzle when you try to think about it on in terms of the in terms of the world sheet because you see this at this vortex solution which is you're thinking about some minimum energy vortex used to add another dimension then the world sheet of that string is just minkowski space two-dimensional minkowski space time and what we're saying is that there's some supersymmetric theory living in this two-dimensional minkowski space time that has to preserve supersymmetries and to broken supersymmetries now the question is that's not supposed to be possible so how is it possible now the question was actually answered by a paper by Hughes and Paul Chinsky which I'm going to tell you about in a moment but when I looked at that paper for the purpose of this talk I noticed in the in the acknowledgments that in fact the question was actually posed to them by Luca Mesonchesco he asked them this question probably sometime in 1985 and at some point so my guess is that Joe didn't know the answer immediately and he had a student eventually Hughes and so he said why don't you have a look at it and so this became the issue of partial breaking of global supersymmetry the point is that as I say the reason there's a puzzle is that the standard supersymmetry algebra doesn't allow for partial breaking of global supersymmetry and that was demonstrated by Ed Whitten in 1981 but the thing is there is a subtlety because with any broken symmetry strictly speaking if you break a symmetry then the charge isn't defined the charge you're supposedly breaking charge that supposedly a broken charge isn't really defined because of infrared divergences so what you really have to do if you want to prove things is you have to look at the current algebra not the algebra of the charges now in practice it's actually okay to look at the commutators of a charge one charge with a current because the singularity in the charge basically drops out when you take the commutator in this case it's the anticommutator because we're looking at supersymmetry charges so you really should start with something like this and you see the stress tensor now appears on the right-hand side if you integrate you're gonna get the momentum and well I've got some of this some stuff in yellow which you can't read and that's deliberate so it's if somebody would ask me a question I which needed me to read out to you what's in the yellow or you can actually read it there with a string of terms and in anything else but okay so at the point is it leads to the same the same conclusion but then what they realized was that was that actually that's not the case that's not the algebra that's actually relevant to the case in hand and the because there's another possibility you can add in an additional term with some constant here and if that's not equal to 0 you see if if we're just and there's a sigma 3 here which means you can't simply sort of absorb this term into that term because it's you know it's different sign according to different terms so it's and if you in fact look at this and work out the implications it is indeed that you break half the supersymmetry and for reasons I'm not going to go into here but the point is that that's actually what you need to be the case in order to get the green short super string the four-dimensional one to be the effective action in this case now that lead in fact already in that paper they're asking themselves the following question the point is that that's a two-dimensional example of where you have this partially broken global supersymmetry and they thought well be wouldn't it be more interesting if you could do it in four dimensions and the way to do that they thought was to say well we did it in two dimensions because we had a string what kind of object do we need if we want to do it in four dimensions well that would be a three brain now fortunately it turns out that this Susie Abelian Higgs model actually exists already in six dimensions that's maximal so you can look at the whole thing in six dimensions now in six dimensions in four dimensions it was a string five dimensions this is membrane six dimensions it's a three brain so yes you have some kind of solution this vortex solution it's it's it's a three brain that has to be some kind of effective action for it let's try you know the write down the obvious thing just kind of copy green Schwartz you've got to have something along these lines here and then you come to the point kappa symmetry how's that going to work now I'm focusing on this because actually before Joe's paper came out in 86 I've actually been working on this problem with Luke Mesonchesco I think in sometime in 1985 and he'd been visiting Cambridge and it was you know after greenish warts and kind of it seemed obvious that now a greenish warts did you know ten-dimensional super string what about eleven dimensions can't we have a membrane and we sat down we tried to so there was an 11 dimensions a different problem but we had the idea of course it's fundamental fundamental string should be fundamental memory we couldn't get it to work because we couldn't generalize we were trying to generalize the self-deal world she vector and all complicated current nonlinear ways didn't work we then went to speak it was during a conference lots of string experts around we go to speak to them and they say what are you wasting your time for of course you know you can't you know that that theory is not going to work course it doesn't work you know forget it strings as you know membrane brains that you know that that's that's that's history well the point is that we had no reason to really believe that it would work so we stopped but Joe knew that it had to work because he had a model explicit model where at least for the in you know it wasn't in eleven dimensions but at least in the six dimensions it had to work there had to be an effective action therefore there had to be a way of making this work and he really they worked out what the way was what you should just do is you say you abandon what green Schwartz did you actually rewrite the whole thing in terms of a parameter that's a scalar and that also works for the green short super string and it's far simpler so when green Schwartz and Whitten when they when they reprinted their book 25 years later I mean ideally they should have taken the opportunity to simplify that section so and the other point about this I'm mentioning this is because I had been as I say I'd been thinking about this problem but you know the end the research part was over we start teaching courses and so on and at some point I was going to come to a conference here one of the ones like the one that's going been going on now and the day before I was leaving I was just looking at the journals and this is pre-internet days of course and there's physics letters B I think I looked up and I looked at the journals and I see Hughes, Liu and Polchinski supermembranes and in fact because they're tight their paper was titled supermembranes although they actually concentrated on the super they were using membrane as a general term and then I looked through it and I saw that this is what they done is I realized immediately you know that was the that was the problem I mean we had been led astray by we've been told never trust the experts that was what I learned from that don't don't take too much the experts tell you it can't be done you know don't believe them but another sort of rule you have to take from that I learned is that it's nice to have a physical model so at any rate now Joe had done it at least in this particular case it was clear rather clear that it could be done in other cases so in fact so I arrived here and I went immediately on arrival to the office of either Eric Berks of or or again says again I don't remember which one and we had a procedure we sat around we put each put our on the board we wrote down a problem that we would like to work on and then we had a democratic vote as to which one we'd work on and my problem I put down 11 dimensional supermembrane and it got voted down well it got vetoed rather than voted down I won't tell you who vetoed it but not these not the collaborate is here but the person who vetoed it eventually left we've written a paper with him so he's happy but but then we had one day left and so I said now really it's this one so one day we you know we found what it was so basically yes you can find now supermembrane action and the caposimetry works in the same way as he did in the paper of Joe and in fact in general what you what we discovered is that you need you need an identity which is like the identity that I wrote down previously but now it's actually a series of them actually see 11 identities which have to be satisfied and it turns out as we as we showed I think that it's actually works in four five seven and 11 dimensions so that was nice we had our one in 11 dimensions but you could also do it in in five notice the five would be relevant because that's that that's that's basically three brain that's essentially the one in that's the same that would essentially be the case in the in the list that Joe and hues and hues Liam Pochinsky so that eventually led to this brain scan now to be called the old brain scan and so it was rather clear that you could guess which ones were going to work by simply asking yourself in which cases do you have enough fermion zero modes to get super symmetry on the world sheet when you have equal numbers of bosons and fermions and that already gives you this this actually this list but then we wanted to prove that was the that was the only possibility and what you have to do is you set it up you have a you have a three form you have a some kind of p plus two form now in super space and you have to show that that's non-zero and closed when is that true in the end we ended up using the computer to do that actually but you know gamma matrix stuff on the identity on the computer although it's actually pretty easy to do it by hand now but at the time we did that by computer and so we ended up with this and you see so there are these four sequences and one of these sequences of course the complex one is essentially the hues Liam Pochinsky one the one you can realize in terms of vortices now that immediately leads to well perhaps not immediately let me just say well yes will lead soon but some first of all I should just point out that another issue is is that in the in the context of this half supersymmetry breaking you see Witten and Olive what they looked at was they looked at a field theory and they looked at field theory solitons and they showed that you get half supersymmetry breaking the space-time supersymmetry breaking in the way I said earlier what the hues and Pochinsky paper was essentially purely from the world volume got a world volume algebra how do you break superset half supersymmetry on that so that was what they did but now you have a situation where you have a space-time algebra the supersymmetry algebra but you have a world volume theory what's going on in that case so what's going on in that case is that so you you clearly need to have some kind of topological charges appearing from the world volume point of view now but how does that happen well the reason it happens is because the term that you have to add this extra term you have to have in all of these actions which is I mentioned it was a vestimino term some topological significance isn't actually manifestly supersymmetric and that means that the algebra gets modified and if you look at what it is it gets modified in this way so for the super membrane you get an extra charge in it which as you can see would be infinite if you had an infinite membrane but supposing you just periodically identify you have a sort of two torus then you see it's just essentially the rate that the volume of that two torus the area of that two torus and then you can see that you get half supersymmetry breaking and that's a general thing whenever you get these brains so it's another lesson in some sense whenever you get these brains appearing that preserve supersymmetry there's going to be some kind of charge in the supersymmetry algebra and it may not be won't be central but they'll be some kind of charge so that's another lesson I learned from this and this is really because of the relation between space-time and world volume supersymmetry this is really equivalent to what Hughes and Polchinsky did some sense it's really rewriting what they did in another in another form so that's another thing I learned from Joe now as I said you can there you realize a lot of these you've got these brains now these brains can you can realize a certain number of them as solitons and so vortices was the case that was studied by Joe but you can have the other ones kinks and instantons that gives you three of these series what about the last octonionic sequence well I was at that time I thought well I shouldn't be looking for solitons there because this is the fundamental one all those others are solitonic this one is fundamental but on the other hand it's clear that there's a and also there's only one candidate theory and that's supergravity theory so now it's clearly looks like a different game but it's obvious that so if the suit so even if the super string is fundamental so you would think it's still still should have it still generates gravitational fields so there still has to there still be some kind of solution that you can find that is sourced by that string take the 2a string so in fact that solution was found in 1990 and it was shown later that it actually lifts really if you look at it in one higher dimension in fact is the 11 dimensional supergravity membrane solution that was found by Duff and Stell in 1990 so here you had the situation where you have apparently look like fundamental but now we start having look like brain solutions and in this case this is not even a singularity the singularity is in fact behind the horizon now this raises a kind of issue about if now we're looking in the context of he already arose in the context of black holes people were asking even before this and the in the relativity literature you know when is a black hole a soliton and there were lots of disputes about this and I think that Gary Gibbons was basically the person who sort of led the way in trying to specify you know what kind of conditions you should have before you can before will allow you to use the word soliton when you start writing down some black hole and that can be generalized to brains and so some of the conditions some of the conditions you would you would want first of all you'd like the energy density to be saturated you look like you'd like there to be a bound on the energy density which is saturated BPS type bound because that gives you zero temperature then you'd like to have it boost invariant in the brain directions otherwise you boost you get different different solutions and that's only true if the energy density is equal to the tension and I'll come back to that point at the end and you usually preserve some fraction of the supersymmetry if you have in a supersymmetric context usually a half and there's some prototypes of this which were discussed already very early in the in the relativity literature in particular there's a very nice paper Gibbons and Hull from 82 on that but there were lots and lots of other ones later and just to summarize I have an executive summary here which goes on the lines of what I was saying really at the kind of the beginning was just if you have a people if you have a form gauge field in supergravity theory then what you should expect to find is some kind of electric black brain solution p-brain and it'll have a magnetic version to with a d minus p minus 3 and in some sense in the above senses they're both solitonic so if you look in 11 dimensions in addition to this to brain solution if you work at what that is there should be an electric 5-brain solution indeed that solution was found by Gouvernein 92 and in that case in fact it is it is actually strictly non-singular solution there's no singularity even behind the horizon so the the singularity theorems of Hawking and Penrose don't apply necessarily to brains okay now I'm going to continue along the line of these black brains and in a moment or two but I have to take a few minutes out just to discuss another paper by Joe this is in 1989 with Dai and Lee so-called new connections paper first of all and you'll see the relevance of this as I move along the the idea was that it was t duality was a was well established property of string theory the idea is that if you compactify on a circle the simplest simplest version if you compactify on a circle of radius r then if you look at if you flip the radius to 1 over r in natural units then you will simply exchange the collude decline modes with the winding modes and then it will look the same so it's actually a symmetry and so that's the case for the bisonic and heterotic stream but point is it's not always a symmetry and this was pointed out in this this new connections paper in particular they started papers two parts it's the one is where they look at type 2 super strings and they showed that type 2a actually maps to type 2b and there's a second part which is on open bosonic strings mostly on that and so they for example you take 26 dimensions would be the critical dimension but the thing is about open strings there's no winding modes so what's going on what they showed was that if you do the same r to 1 over r then you take r going to 0 you get back to 26 dimensions but now your strings the open the end points are all stuck to a kind of hyperplane with co-dimension 1 so that would be a 24 brain and in fact they called it they called it actually a Dirichlet 24 brain and that's the word D brain actually comes from this paper in 1989 and also from this paper in 1989 they pointed out at the end that the tension would be it's a non-perturbative object the tension would go like one over the string coupling constant which makes it semi-perturbative because usual solitons it was like one of the string coupling constant squared if it's perturbation theory you know independent of the coupling constant so the semi-perturbative it means the full dynamics can't be can't be discussed you can't actually move it it's got infinite energy but nevertheless you can look at the fluctuations well okay they didn't make those remarks in the end of the because it was a kind of a little bit of a throwaway comment at the end of their paper because there was some discussion of how that would work in other strings super symmetric strings and they were negative about that so so in fact even Joe himself didn't really you know never really pushed this point and for me this is one of the kind of mysteries of string theory because for years this paper was around I was even carrying it in my briefcase for years and I had it when I was working on with Chris Hull on later what I'm going to come to you dualities and Chris Hull knew a lot more string theory than I did but I knew one more thing than him was that I'd read part one of this paper died you Pogchinsky and I told them 2a2b we don't have to worry about that that's already been done I didn't look at the open bisonic strings I had looked at it in the past but to my deep regret I didn't read that paper properly again but also my surprise in the years between here and 95 when I talked to string theorists and tried to convince them they should just think about brains they always said brains you can never get brains in string theory impossible well here it is back in 1899 in plain black and white you know there's a brain it's why did nobody tell me yes you can know it seems that there's there was a complete amnesia in the string community and I I don't understand why and even Joe himself didn't seem to be saying anything about it he could have piped up but you know I'll never know but why he didn't but at any rate so it's a very important paper I think and if I'd read it more carefully I said at the beginning I was telling you how Joe influenced you know Joe's impact on my work well this is you know this is where I had an un missed opportunity of having learned more from Joe because I failed to read to the end of his paper okay so coming back to this the idea of now we've got so we had those old brains and now we've got some new brains in his super gravity models and you see you can how do you differentiate them all well what you can do is you can look at the small fluctuations since they're super symmetric then there's got they're always going to fall into super multiplets of some kind and so you can look at them in terms of what are the world-volume super multiplied on this you know you've got infinite brain you have small fluctuations some kind of super symmetric theory with some super multiple what is it well there are only so many kinds of super multiplets of course we know all of them so there's first of all scalar super multiplets this has to be non-gravitational course too because we don't have gravity on the brain so there's the old scalar super multiplets you have scalars and your spinners now all of those cases are just the old brain scan but now we have some more because some of these if you look at them you discover they actually have vector fields vector multiple so they have vector fields now this is pre-D brains so but they would be called D brains in the future they're now called D brains but they won't call that then and and in fact there's in the second if you look at this there's a six-dimensional and asymmetric tensor multiple that also appears and it appears on the NS5 brain that was also in this paper by one of the papers by Callan Harvey and Strummager and that also is true for the other non-gravitational five brainless as it was pointed out in the paper of Gary Gibbons and myself a couple of years later and of course that was eventually going to be called the M5 brain but we didn't know anything about that then but at least now you had a kind of distinction another way of classifying all the possible brains and the old ones well that's just the scalar super multiplets now this raises an interesting question you know do all gravitate non-gravitational Minkowski space field theories arises fluctuation on brains a lot of them but I'm not sure what the answer to that question is I always thought it would be nice if the answer is yes so a lot of my work in the past has been directed to showing that certain obvious objections can be surmounted but we'll leave that point a little bit to the very end okay now I want to move on to we got all these new had the old brains that we got a lot of new brains you know it's getting out of hand it's starting to look like you know where you had just a few particles and now in the 60s you go to whole stacks you know thousands of particles you've got some kind of organization is required here well we have all these dualities and as I mentioned you have heterotic duality and I told you about the simplest case but if you compact divine a six-tourist well there are lots of parameters for a six-tourist so it's it's more complicated but here what you get is the symmetry focus on the point here which is so 622 that actually includes the R goes to one over R in all of the six cycles of the tourists but you know a lot more and the super that well is an effective super gravity the effective theory is invariant under so 622 but what we know from T to a from string theory is that's not a symmetry of of string theory it's an artifact of super gravity theory the low-energy approximation but not entirely because string theory does preserve some of it it preserves a discrete subgroup which is so 622 z and that's the T duality group in string theory so string theory preserves some of those dualities that you have in super gravity now just look at this i have a so 622 and you know that's broken to this discrete subgroup there's an sl2r there too what about that shouldn't that be broken to some discrete subgroup well if that's the case that would have to be non-perturbative because if you look how that acts on the dilaton you see basically it takes the coupling constant to one over the coupling constant so that would have to be non-perturbative but still you could you could think well why not and in fact one of the people who thought why not was your um if you can read it there or you can you probably can read them I can't read them on the screen but there you are your your current director of ICTP Fernando was basically among the you know on this paper which was the first paper to conjecture that and there was some you know a lot of evidence for that appeared later and so that was kind of somewhat believed by the time you know 1993 uh around that time so in 1994 I got together with Chris Hull and we said to ourselves well that's n equals four now what about n equals eight but if you start with type two string instead of a heterotic string and then what happens is well you get this this symmetry if you compactify Kramer and Julia pointed out uh in back in 1978 that you haven't this E7 non-compact E7 symmetry and the nice thing is that if you E7 contains SL2 R times SO66 now if each of those sub factors gets broken to a discrete factor then why can't we would it not be make more sense if the whole thing gets broken to a discrete subgroup and in fact we argue that on the basis of direct quantization conditions um and also irreducibility but uh so the idea here is that but still of course it's conjecture um that the idea then it was of course it'd be non-beturbative um and the idea is so E7 is broken to this discrete subgroup and it would then unify the s duality with the t duality so that was the idea of that now it had some consequences and one of the consequences that we pointed out in our paper was that if you look at the field strengths in n equals 8 supergravity the two form field strengths there are 28 of them so with the 28 hodge duals that forms a 56 and that 56 is actually irreducible multiple of E7 and if you look at the decomposition with respect to this SL2 rns of 66 it breaks into a 212-132 and that's basically the 212 essentially are electromagnetic the 2 is because they're s dual pairs and one is electric and one is magnetic and but they're from the nibbush-watt sector of the type 2 string and then the other ones are from this mysterious remonde-remonde sector of the string you have all these p-form gauge fields which apparently don't couple to anything in the string theory but now it seems that if u-duality is correct they actually have to couple to solitons because once you believe that you've got some solitons here which in fact you know you do then because of the irreducibility of the 56 you have to have all of them so u-duality would imply that in fact there are some remonde-remonde solitons and of course where do they come from where do all these charges come from well they come from brains in the higher dimension so that means there have to be brains that couple to all the remonde-remonde fields and that's what we pointed out in 1994 now I'm getting towards the end at this point we still don't have I'm getting towards sort of leading up to the Joe's D brain paper so in 1994 we so there was it was clear that there was something going on with 2a and 11 2a string 11 dimensions and in fact an early sign of that had been the fact that if you start from this 11-dimensional super membrane and reduce you get the 2a super string action a world volume action and I pointed out in early 1995 that you could interpret the zero brains and the six brains as the Klutz-Klein modes in the 2a theories Klutz-Klein modes and Klutz-Klein monopoles of some higher dimensional theory in 11 dimensions some super membrane theory that paper was rejected it was rejected until I didn't know what to do about it but then Ed Whitten's paper appeared and I got a message back from the the editor of the journal and saying are you still interested in publishing your paper of course by that time it was too late to make any changes to it but of course and of course Ed Whitten pointed out that if you take the strong coupling limit of the 2a string theory then you get some some 11 dimensional quantum gravity theory and call it M theory why not and I think he offered a suggestion of meanings magic mystery and membrane but of course you know which one I'm going to choose of course he did a tremendous amount more in that paper than a tremendous amount more in that paper that's a sort of magnificent paper which shows how the all the string string theories or at least some of them I guess there's still some to come at least the 2a and the 2 type 2 in the M theory you get unified but what's not in that paper is any mention of brains now a couple of months after that Mike Duffer myself were in Baltimore when Ed showed up for a conference and we walked around the campus and the two of us two of us were trying to persuade the third that you know how can you have this brilliant unification but not have brains I mean you have to have brains and he said no no no brains you know don't want any brains the only brain I need is this one no he didn't say that I'm just joking but he could he could have said it would have been a powerful argument you'd have to admit but partly motivated by that you know I titled the topic of my contribution to that workshop brain democracy on the grounds that if you have brains you have to have if you if you have you duality and dualities you have to have brains and in fact as I said it's a brain democracy but of course as I pointed out actually all brains all brains are equal but some brains are more equal than others and I think that's the kind of status that has been ever since then and because in practice it's you need in principle all brains are equal but in practice of course some of you know you get you make progress and others you don't make progress now we come to the end of 1995 and so Joe comes back with his ideas about D brains he's now realized that actually what he said in 89 about it not working for the type two strings it is going to work and so you know that's another amazing paper and of course subsequent to this we now have a kind of classification of these brains again according at least in the string conformal brain so if you're a if you're a string centric point of view so you have a democracy I guess it's like the world you have a democracy you know United Nations but then you have particular points of view from individual individual countries you know they in principle they should all be parallel transported to another one and be completely equivalent versions of saying the same thing you know like documents some promoting something and you have it in one language another language is supposed to be exactly the same thing but we don't know so now we have a separated into essentially how the tension behaves with respect to the string coupling constant and so we have the fundamental ones the Dirichlet ones and the solitonic ones and now we have a sort of a different brain scan here with all of these other brains appearing of course there are more that I haven't put on here and we now know so these carry p-form charges they're one half supersymmetric they're fluctuations of vector multiplets and more to the point the vector fields on those multiplets couple to the string end points and that's a nice picture and I'm going to come back to that in just a moment in fact I'm almost at the end of this tour you'll be I should be finishing soon so I'm almost at the end of course the point is I could go on I mean I have to stop somewhere and I'm stopping here on this paper of course there's a tremendous amount of polish from this paper so in some sense it is a natural point to stop because where would you continue I mean it's obviously I should leave that to you know to the next so somebody else I just just one further point is of course that when I saw Joe's paper sometime soon after that I realized that you should do something similar in 11 dimensions and so if a string can end on a D4 brain that somebody would lift to an M2 brain on an M5 brain and there were particular reasons for that Andy arrived at the same conclusion virtually at the same time but we had completely different reasons for it so I don't know whose reasons are right but hopefully one of them okay so I'm at an end and I'll just end with one further transparency so rather than end on so I want to end with a with a suggestion which has intrigued me and I sort of this point dawned on me actually a long time ago back in 2005 on the 100th anniversary of the Einstein's paper on relativity because I was asked to give a talk a short talk actually 20 minutes at a conference in England somewhere to celebrate that I was trying to think of what I could say and I wanted it to have something to do with brains and eventually this point occurred to me and the idea is as follows is that you see I pointed out beforehand you know I asked this question are all matter all quantum field theories can be realized as fluctuations of brains well at least we have a lot of examples of that and we even have de-brain constructions of the standard model so but and within that kind of context you have a general kind of picture that you have supergravity fields in some bulk and you have matter fields on the brains so we do have a kind of natural way of distinguishing between what's matter and what's gravity in this context it's a rather physical way of saying what the difference is and if you take this idea seriously just take a simplest case of a d3 brain never mind the standard model just electromagnetism how would you model that will you have a d3 brain because you need three space dimensions and you need a de-brain because you want to have electromagnetism on the brain so you need your vector field propagating along now the point is is that the in that context the infinite plane of brain is actually the vacuum for the electromagnetic fields those electromagnetic waves that are moving around they're stuck on the brain they can't get out so the brain is in some sense a medium for them if you like it's the kind of it's an ether now isn't that inconsistent with special relativity didn't Einstein say there's no ether well no he didn't say that if you look up the paper all he said was that it's not necessary for his analysis which is indeed was quite true but that doesn't mean it doesn't exist but if it does exist it would have to have certain properties it has to be compatible with you know Michael Somalia experiments and so on and that means it has to be boost invariant now when is a brain boost invariant well take the simplest case of a string and suppose you have energy density epsilon and you have tension t well the wave velocity on the string is that's a simple you know undergraduate mechanics thing it's a simple t over over epsilon well normally it's the mass density but I replaced it by the energy density so that's where there's a c in there so and the point is a boost invariance means so you've got this wave propagating along the string you boost to a different frame you're going to change that velocity it won't be boost invariant unless that velocity is the speed of light so if you put v equal c it'll be boost invariant but what is that that's when the tension equals the energy density that's a bps property and in that case you see the the wheel sheet stress tensor you have an energy density you have a tension the wheel sheet stress tensor is then proportional to the two-dimensional two-dimensional in this case minkowski tensor t mu nu is proportional what's the constant of proportionality it's the constant c in the Hughes-Polchinski introduced to explain the pbgs that's what it is and so I think I'll stop at that point thanks very much thank you very much Paul for such a original talk and even more original ending which is did I end at the right time yes very very it's okay so any questions comments disagreements yes oh disagreements come on I actually have two questions and two are not connected so one question is that you spoke about the action which later became the wall volume action for the m2 brands so is there similar thing for the mpi brands and why people didn't consider at that time when you were doing the wall volume action for the m2 brands yes well it was considered in fact it was considered by me but among others but the point is it's it's rather complicated and that was really a problem that was really only solved by the it's it's well it was solved by groups here I mean if I get all the people on the papers now it is Demo Sarrick and it's one of them and you know I yeah I won't go through you know I won't go mention names because you know I miss some out and then that's terrible I know Demo was was on the paper of course so yes so so the point was that was a difficult problem actually it was already difficult just for the D-brain to just construct the action was already it's in the supersymmetric case and so that that was took quite an effort so it took some a few years to do that with in fact that was that was a case where I was I worked on that with Eric Bergsoff and we successfully completed that along with some other people more or less at the same time but the five brain case is much more difficult partly because it has non-linear self-duality condition so in fact it involves solving problems of how do you deal with self-duality conditions and even non-linear ones right thank you I actually have another question you pointed out that you already I mean in your paper in 95 you found the connection between the Kaluzak line modes of 11 dimension and zero prints of type 2a well I can conjecture it really yes and that that was also used by by we tend to found the relation between the coupling constant and the radius so yes good question no but the answer is the reason is this it follows is because well if you read that paper you'll see that there's lots of gaps in my knowledge of string theory but the point was one of them was that I think a lot of us were under the following impression you have a membrane wrapped you wrap a membrane around an extra dimension but if you try to contract that extra dimension that extra dimension down to zero size then the membrane contracts down to zero size has zero energy and therefore its tension has gone to zero and you get some kind of tensionless strain that didn't make much sense so we had the idea that well yes you had to you had to be you know so it somehow some stabilization process we didn't know what to do about that of course the answer to it is that what you have to do is that as you take as you contract zero size you also move to the string frame metric and that kind of compensates for that effect and so then you can make sense of the of that limit but until you make this change of conformal frame you don't make sense of that limit and because that's in Ed Witton's paper and not in not in mine because or in fact any of the previous ones because I think we hadn't appreciated that point in yeah more questions so curious did you come back to the conversation with Witton in Baltimore after that pardon did you come back with your conversation with Witton no I perhaps I should have remarked that in fact although he wasn't convinced by us he was convinced by Joe's D-Brain paper so when that appeared of course you know he jumped on the bandwagon I think it's the probably one of the few times that he's been jumping on bandwagons but you know most of the rest it's us jumping on his bandwagon but but yes he definitely was and of course he was immediately almost immediately writing papers on it because then we had the idea then we had this paper on the Coincident Brains and the UN and so on and he worked with Joe Polchinski on dualities and heterotic and type one and so on Chris Hull also worked on that you know I that would have been a natural thing for me to discuss beyond that but as you I'm glad I didn't prepare that but it would have gone over time very good okay so I think this also being a very good start to this tradition of Joe Polchinski's colloquium as typical we have refreshments outside for everybody and we always invite the the students the diploma students to come and ask more private personal questions to to the speaker in this case I hope that Paul doesn't mind and then in the meantime you are all welcome to join us and so let's think more again