 So I'll talk about supersymmetric KKLT, which is a string theory attempt to construct the Cedar Vacuum and Neoparton-Galsteinian cosmology, and I have many collaborators, as you see, in the recent couple years. So let me try to describe the current picture in experimental and theoretical physics. So all kinds of things are happening, and we are expecting to have either b-mode detection or a new bound during the next few years. During the next few years, we expect either discovery of supersymmetry or new bounds on scale of supersymmetry breaking. And then we have number of objects which are now firmly established. We know from CMB anisotropy that the scale of delta rho over rho is approximately 10 to the minus 5. We know more or less inflationary tilt of the spectrum. And s equals approximately 1 over 2 minus divided by n, where n is the number of e-foldings. And we know that dark energy is well represented by cosmological constant, and the number is ridiculously small. And moreover, during the last few years, it become even more close to the fact that cosmological constant may well represent dark energy, because the current equation of state from Planck as well as Supernova is much closer to minus 1 than it was few years ago. And the only known way to address the issue of this incredibly small number is to appeal to string landscape and anthropic reasoning. And if we take all of these into account, then we want to describe it bottom up. We have these few numbers which we already know and two numbers which we expect to know or the bound on them from LHC and from B modes. So the question is, which I'll try to address, can we describe all of these using only what I'll call conditionally primordial sector of supergravity, which include the inflaton and the Galzino multiplet. And the answer is yes. Now the picture which I have here is the one from the release of Planck data. Oops, sorry, let's go back. And the two yellow stripes which drive from 5 squared model for 1650 volts are here and they are going in the heart of the Planck data. And those are the model which I will describe there, known as alpha attractor models. In terms of these models, we will also try to describe the flexible value of B mode and the flexible value of Susie braking all inside one small sector. So this is, there was a string phenomenology workshop a week ago in Madrid and this is a slide from Keck and Bicep, which gives the likelihood of what will happen during the next, by end of 2015. And I'll just add to this that Bicep Keck paper will be out in couple of months. And so what you see here is the projection of their future bump. It has a particular position and particular shape and this might change because they will add this 95 frequency to the data. And this is just to compare the result from February 2015 likelihood. And what you see here, the most important thing is they're both for R approximately 0.05. However, what they have here as of today is that R is highly non-excluded. It starts with 0.4. Whereas in this picture, they made an assumption, they don't know the results yet. It is much lower. So what may or may not happen, that the position of this peak and how well is R equals 0 excluded, will see the trend in just couple of months. But of course, much more reliable data will come significantly later from Bicep, Keck, Spider, and other experiments. So therefore, in the total picture of things, checking on supersymmetric kekeltiaplift is what we were doing in the last year. And so the stringy derivation of the Ceter vacu is based on the existence of anti-dissuery brain, which we were explaining in the paper with Katra, and Linda, and Maldesina, and Macalester, and Trivedi. And the main thing which was happening here is that there is a contribution from Dirac, Born-Enfield, and from Vesumina. And for D3 brain, they cancel under certain conditions. Whereas for anti-dissuery, there is a constant contribution to the energy. And it is negative to the Lagrangian. Therefore, the energy is proportional to the work factor. And this was known as an uplift of the vacuum in kekelti construction. So what we have done recently, we kept fermions on the brain. And we made it supersymmetric in the following way. So instead of just keeping scalars and vectors, we give a full attention to the presence of fermions on the brain. And therefore, we started with caposymmetric action in superspace. Everything is perfectly supersymmetric. We use the orient default condition. And therefore, the result of our paper with Maldesina, Trivedi at all, in presence of fermion is confirmed. So for D3 brain, the total contribution to the energy cancels between Born-Enfield and Czern-Simon term. Whereas for anti-D3, they sum up. And we are obtaining this beautiful contribution, which is actually Volkoff-Akulov action for the Galztino fermion. So this is a manifestly supersymmetric Volkoff-Akulov action, which is supersymmetric version of kekelti uplifting, which was worked out in all details recently. Now, ineffective n equals 1 supergravity, Galztino multiplet is a chiral multiplet satisfying the nilpotency condition that s squared equals 0. And the simplest case is when you take the superpotential proportional to this field, the Kehler potential is canonical. And as a result, you have a beautiful positive universal contribution to the energy. Now, there was a discussion, in particular, during the Sink phenomenology workshop in Madrid about the difference between the situation with many anti-D3 brain versus one. And I'll try to summarize. There were a number of talks on this. So the conclusion, the current conclusion, which many people share, is that there were over the years numerous claims of instability in the literature. But they were valid only in case of many brains, because the conditions were that the G string is much less than 1, whereas G string times the number of brains is much larger than 1. And you may have seen in the literature fatal attraction singular to the bitter end, obstinate tachyons, et cetera, good and bad singularities. Those questions have been asked. And with current understanding, we believe that these debates are not relevant for KKLT uplift to the sitter, where number of brains is different from one. Because if we have one anti-brain, we can make it the sitter. And this is what is relevant. So with regard to single anti-D brain, there were two developments. First, in the supersymmetric case, I explained to you, the case is perfectly clear. And there is a supersymmetric version of it. And this works for single anti-D brains. And therefore, for the sitter. There was also a paper by Polchinski and his collaborators, where they looked at effective filter description of anti-brains. And they also realized that for a single anti-D3 brain, everything works nicely under condition of small string coupling. And so the conclusion at present is that if you are interested in stringy version of KKLT mechanism, look for a single anti-D3. And in this case, there is a universal role of Galstina multiplet at the minimum of the inflationary potential. We are working with supergravity. There is always positive Galstina contribution. And of course, what is well known, always negative Gravitina contribution. So M squared corresponds to Susie breaking via Galstina. And the second term is Gravitina. And so Volkoff-Akulov non-linearly realized supersymmetry is spontaneously broken by construction. And therefore, in this framework, a tiny cosmological constant results from incomplete consolation of the positive Galstina and negative Gravitina contribution to supergravity energy. And because all of these will be done in the context of models which are in perfect agreement with Planck, I would say it is rather interesting. So what is the nilpotent carol superfield? The usual superfield has a scalar component, a spinor, and the auxiliary field. And then in addition, we impose this condition as squared equals 0. And there is a solution that there is no fundamental scalar. A scalar is by linear combination of fermions divided by auxiliary field. So this is the Volkoff-Akulov action written in 72. There was not too much attention to it. There is only a fermion. Then it was realized by a group of people that instead of using the non-linear realization, you can use a simple carol multiplet, which however is nilpotent. And for those of you who are interested, the best reading is Kamagorsky-Cyber. They give a very nice explanation. And then it has been used in cosmology, which I'll tell you more about. And then you will see also in the talk of Anvelinde. So the connection to D-brain, I explained. And this is basically that when we compute the Dirac-Born-Infeld investment in a term in D3, it is they cancel. In anti-D3, they sum up. And you see, this is the Volkoff-Akulov action precisely, which is coming from the D-brain. And the action for some of you, why we use the word non-linearly realized supersymmetry? Because first of all, there is a negative contribution to the Lagrangian, which is positive contribution to the energy. There is a kinetic term. And then there is a bunch of higher derivative terms and lots of non-linearities in the fermionic part. And this is the most important thing, which is not widely known, that the supersymmetry transformation of the fermion contains a constant fermion and something which is quadratic in fermions. And this is the original transformation of Volkoff-Akulov. Now it is used in the context of KKLT uplift to desitter. And then the question is, can we make it local? And I'll try to explain what happens when we try to go to local story. So n equals 1 supergravity for chiral and vector multiplets is known. If you know what the scalar potential and superpotential, you can give the complete action. Just open the book. However, we just learned that if one of the multiplets is nilpotent, and you know K and W, you can only produce the bisonic action. The fermionic one, which includes the gravitina-galzina interaction, is not in the book. And so we are constructing it now. So even if you take the very simple story, just a superpotential linear nilpotent multiplet, you can easily write the bisonic action, but not the complete one. So this brings me back to 77, a very famous story of what is cosmological constant in supergravity. In view of dark energy, it is an important reminder. So it is known to be negative. If you don't have scalar fields, cosmological constant is always negative. And there is an anti-desitter. So supergravity with positive cosmological constant without scalars was not known. The new supersymmetric K-K-L-T uplift procedure indicates that such a scalar independent decider supergravity does exist. And in fact, we are about to show you. So here is the Thamson's formula. This is the curvature term, gravitina-kinetic term. And then if you add this negative term to the potential and you pay the price for using the same parameter in the quadratic term for gravitina, the action has, first of all, negative cosmological constant. And secondly, it has local supersymmetry, which is broken spontaneously. And the cosmological constant is negative. Spontaneously broken means that the transformation of gravitina has a term which is field independent. And then it is more common today to interpret this mass-like quadratic term as it is a massless gravitina, but in ADS-4 background. And it was always known it is negative. So on the other hand, we look around us and we know that there is a dark energy and cosmological constant is positive. So what can we do? So I'm moving to this title, De Sitter Supergravity. And a year ago, I wouldn't know how to construct it. It turned out that when we were trying to do our best for Planck, we came out with understanding that using superconformal theory, it is possible to construct the action. Now what we are doing with Berkshoff-Riedmann and Van Proen, we will present a complete De Sitter Supergravity. So this will be the form of the answer. You have the usual curvature. You have a gravitina-kinetic term. You have a coupling between psi, mu gamma, mu gravitina, and Galztina. You have a kinetic term for Galztina. You have a nice positive cosmological constant. And a mass here. And a mass is a coupling of gravitina and Galztina, whose explicit form will be given. No scalars. Local supersymmetry is broken spontaneously, but it's different from the case of negative cosmological constant. It is broken in the Galztina sector. So there is a term which is independent on the fields. And this is your cosmological constant. And it is positive. So if we take a global Suzy limit of this theory, which means we send the coupling to infinity, the local supersymmetry becomes global, gravity decouples. So the whole term here goes away. And here we are reproducing Volkoff-Akulov-Galztina action from 7 to 2. Now it was 40 years to switch from negative to positive cosmological constant in supergravity without scalars. And the new motivation is because we have this acceleration to describe. And therefore, that was the interesting story. Now let's do the following. Let's gauge fix local supersymmetry. Let's say we take a gauge where Galztina is absent. And this is a very nice and beautiful answer. So you have supergravity. And you have a positive cosmological constant. And you would say, well, of course, this breaks supersymmetry, except that now we know it breaks it spontaneously. And after you gauge fix, only you get this nice and simple action. So the positive cosmological constant has this interesting origin in this class of models. So let me remind you, how do we break supersymmetry? There are two famous methods. The one which is due to a rifer T back in 75. It is nature to call it engineering. What he did, he invented the superpotential, which depends on three different chiral superfields. And this is the expression. And breaking or not breaking supersymmetry means you have to solve the equation that the derivative in three different directions has to vanish. And if you look at this, you see, when you differentiate over phi 2, you need phi 3 to be 0. But if you differentiate over phi 1, you see that phi 3 squared has to be m squared. Those are inconsistent. And therefore, this engineering tells you, in this model, there is no unbroken supersymmetry. Supersymmetry is always broken. The other well-known case is de-terms use your breaking. There is a phi iri-lopoulos term. But again, you need vectors and scalars. What happens with nilpotent chiral multiplet with regard to dark energy, which is important? If we say the existence of chiral multiplet is the case of natural unavoidable spontaneous supersymmetry breaking, and there is no need to engineering. And I'll try to explain it here. So if I take this parameter, which is my cosmological constant, equal to 0, I will truncate the multiplet in global supersymmetry. So Volga-Fakulov theory was known a long time ago. However, if you have globally supersymmetric theory, you cannot really explain dark energy because you need interaction with gravity. And because the theory is supersymmetric, you need interaction also with gravitinous. And this was not known to exist. So now the case which we have is that m, which is e to the power over 2-time derivative in the direction of Galstina, is not 0. And so now the new point about dark energy and supergravity that in models with nilpotent chiral multiplet, the potential always has a positive contribution, this one, times square root of g, which we need for dark energy. And it competes with negative gravitina contribution. Now this is the main technical slide for you. Look, what means the nilpotency condition? s squared equals 0 actually includes three equations, one which is 0 level in theta, first level in theta, and second level, theta is two component. So let's look at the first equation. It is s times the auxiliary equals psi squared. The other is s psi and s squared equals 0. And there are two distinct cases. If my auxiliary field is not 0, then there is a solution that s is a bilinear of fermions divided by auxiliary. And this actually solves all three equations. If, however, the auxiliary field is 0, then both s and psi have to be 0. And this is what I mean that the existence of this multiplet means I have positive cosmological constant. Because there is no non-trivial solution when Susie is unbroken. Thus, a Volga-Fakulov-Galstein nilpotent in supergravity is identical to universal value of supergravity potential at the minimum. Now I switched to string serialization of the nilpotent Galstina, which is based on URANGA 99 and recent work in progress with Pernand Keveda Angel URANGA. And we just learned that if you look carefully at annulus amplitude in open string and mobile strip, you find precisely the situation where the fermions on the D-brain are there. And there are no other partners, neither scalars nor vectors are present. This is even a better picture, which explains what happens with this orienting folding. All bosons are truncated, and fermions are there. No scalars, no gauge fields. So this is a string derivation of fermion-Galstina. Once we understand the D-brainer region of supersymmetric KLT uplifting, we will apply it now to effective D equals 4 supergravity, where we will use this nilpotent carol multiplet. And it thinks precisely. So it is really strange. We were able to describe inflation, suzibraking, and dark energy. Just having two superfields. One is the inflaton superfield, and the other is this Galstina nilpotent. So the model's alpha attractors, as I mentioned in the beginning of my talk, they are plotted by these two yellow lines here. And then the question is how to describe dark energy. In those models, which with regard to inflation are already good. So in these models, there is this interesting parameter, alpha. First of all, delta rho over rho is easy to build in. NS just happens to agree with the data. And the parameter r is flexible. It depends on this parameter alpha. During the last two years, many people who perform measurements were asking, what is alpha? The one which runs the value of r down from phi squared to smaller alpha. And the answer is, it is a curvature of the modular space. This is the answer we knew from the very beginning. It turns out there is a better and more interesting answer. There are Escher's paintings, which correspond to precisely the geometry which we use in this model. It turns out that Escher had this kind of angels and devils. And this is a boundary of the modular space. And Andrea Linda will describe more the importance of this boundary. And he also had the same type of picture on the disk. And this is just a change of variables. It turns out that the value of the parameter r, where b-modes will be bounded or discovered, is in simple relation to the size of this disk. So that was a good explanation. And so we can have either disk or half plane variables. And those are both manifolds with boundaries. What you see is the size of angels and devils closer to the boundary, getting smaller. It's just a general activity effect. They are here exactly the same as here, in proper variables. And you can read more about it in this paper. OK, here is the picture. This is a numerical values for NSNR for these models. And as you see, in one class of model, we can go from here down all the way to 0, starting from plus infinity via most important and interesting situation. And the analogous story is taking place here, where we have other models. So the ground-based experiments, this is logarithmic scale, they will measure somewhere between 10 to the minus 1 to 10 to the minus 2. And the space mission probably will go to 10 to the minus 3, or as some people say, 5 times 10 to the minus 3. So there is an extremely interesting situation with these models. And the first will be discovered, which are on the top. And then, if they don't see anything, we'll go down. And what is interesting, that if I have a generic N-acoust-1 supergravity, nothing fancy, then alpha is generic. And so the measurement, just tell us what is the size of the Escher disk from the sky. This is just another picture, which represents the symmetry of this geometry associated with the fact that there is a mobius symmetry, where you see if you start it with pentagon or triangle, there will be pentagons and triangles closer to the boundary. Now, it is very interesting. You may have heard a few things about modulus stabilization. How difficult it is to do modulus stabilization in string theory and in supergravity. In these models, it is just excellent because Skelz-Tina is not there. It's a quadratic function of fermions, so we don't have to stabilize it. The other field, which has to be stabilized, is the Inflaton partner. But in these models, it turns out it is extremely easy to do it. Either you don't need stabilization at all for this model, or you can use something which is well known to people who did stabilization of modulate. You just need a bisectional curvature, which sits on the fact that you have both the new potent field as well as the Inflaton field. And everything is perfectly stable and simple. Now, we take the same model, which described Planck nicely. And we want to make supersymmetry breaking in this sector as well as to produce dark energy. And there are two methods we used. OK, I'm finishing. One is reconstruction method, and the other is just taking the most general attractor models. And I'll skip this. So this is just for comparison. We have heard during recent few months, those are string-inspired supergravity inflation models, where everybody understand now that the bicep is not really sitting at five squared but below. People try to do various things to go down. And in some models, it goes this way, in some model this way. And for comparison, the model which I described for you, and the reason why they are in Planck paper is because they start with five squared and just push all the way straight through the sweet spot of Planck data. The advantage at present of these models is that they do everything in one simple primordial sector. There is an infotone and Galatina. The suzibraking is totally independent of the scale of the infotone. That was very difficult to make in the past, but now suzibraking could be anything. And if LHC doesn't find it, we'll just say the gravity is heavier. So we wait for LHC with regard to establishing the parameter alpha in these models, which brings us to smaller r. Again, we wait for b modes. And finally, dark energy is already taken care in these models, because once I have supersymmetry breaking, the parameter lambda is coming out from the imbalance between the Galatina and Gravitina contribution. So those seem to be very useful models. Thank you. Love questions. Hi. So when it comes to a complete string model, so you have, on the one hand, you have the GKP, KKLT type background. On the other hand, you have an anti-D-brain. Yes. But the anti-D-brain also comes with the whole tower of string states, which are breaking the opposite half of supersymmetry to the other side. So it's not clear to me that there is a scale above which supersymmetry is restored. Because if you have spontaneous breakdown, you have to have a scale above which you have supersymmetry. Right. So what is happening here? The Galatina multiplet is fundamental. I don't need a scaler. It is just a quadratic combination of fermions. And it goes with this parameter m, which is free. I am going to feed the data when I hear from LHC and when I hear from b-modes. This is suitable for future data. And in particular, the interpretation of parameter m is associated with the parameter of spontaneous supersymmetry breaking of the nilpotent multiplet. It is an exact statement in this case. Because I have only fermions on the brain. I do not have scaler partners. That is different from everything before. So my question was related to not to the, I have no problem with the supergravity interpretation. I'm just asking, what is the scale above which I have supersymmetry in the complete string theory? Well, this is what we are trying to give more details with Uranga and Keveda. So in complete string theory, if we take this particular setup where we take into account analysts as well as mobius strip in precise agreement with what we see with d-brains, this is how you get this nilpotent galstina. And more details will come soon, I hope. So go ahead, Jesse. So I think I probably have the same question, which is that because you have this nilpotent field, if you get to energies that have order m, then you start getting into a strong coupling regime. So if you get to higher energies than because you have the derivative couplings acting on the gold steno, you now have couplings size that are effectively bigger than 1. So once I get to energies above m, something needs to help UV complete that. So what's the dynamics that you have? This is why we study super string theory. Setting for this nilpotent galstina, it was not known. You're telling me that there's going to be string-like dynamics around the scale m. Yes, it is a string dynamics, which presumably will tell us. It was not studied when there was the anti-D3 sitting on O3 at the tip of the throat. And so it's just not known yet. Yeah. Maybe a very naive question about the sitter, super gravity. Yes, please. As you know, in the sitter, we do not have a globally defined time-like direction, time-like killing vector. Then how do we deal with the super algebra? What's the notion of Hermitian Hamiltonian in this space? Well, Hamiltonian in super gravity is a special situation because we have constrained. I have gravity in the first place. So the Hamiltonian gravity by itself is a tricky point. As of this moment, the reason why we decided to do the local version of Volkoff-Akulov is because in Volkoff-Akulov, the fact that I have a positive constant in the potential doesn't mean much because the constant in the global theory I can remove. However, once I get the time square root of g, it is there to give me cosmological constant. Now, the issue of the Hamiltonian, as always in gravity, is not something of first priority. What is a first priority? The only solution of classical field equations is the sitter and not anti-dissitter. That is the main difference. But when we expand the theory around that solution, there is nothing to expand because we don't have any scalars. So nothing else takes a veff. That is why it was so interesting. Because if we have scalars, we can always engineer an potential which at the minimum of the scalars will have the sitter. No scalars. That is a correct question. Yes, thank you. We can take one more question. Otherwise, we can thank the speaker again and take the break.