People on this Heritage Council are amazing to do what they do for their communities. So what we're hoping to do is come in and kind of put a restaurant in to access the public, get a nice overlook here and that way everybody can come and get the great look of the river that's coming through the Russell Fork and be able to access the beaches along with the walking bridge whenever we can hopefully get that up soon. And today the main reason we were here is to work with the Elkhorn City Railroad Museum. They desperately need funds. We've given from our own pockets our own time. We're very passionate about our communities. We're very passionate about making something happen in this area that can attract people in, re-establish our tax base, re-establish our counties, re-establish our cities. We have to have funds to do that and the way we look at it is why not use the income from the community to get back and rebuild our own towns again. This town was completely built around the railroad. I'm the daughter of a railroad that was on forever. He was over 40 years when he retired. One of my partners, he's a railroad currently through Norfolk Southern so the railroad really hits close to home for us. Elkhorn City is a community that's got so much potential and working together they can really really do some great things here in the community. And I'm certainly willing to help any way that I can. I know a lot of other people, people in elected office feel the same way. There's just such a unique community and so many outdoor activities and such such great people. I mean just the greatest people that that you're ever gonna run into and such potential to see what can happen here in Elkhorn City. And we're here today, you know, I came today just to not only to give them the citation for the Ram Clinic but also to look through the Railroad Museum which is phenomenal. I mean anybody that's interested in railroad and railroad history, they've just got so much here to take in and so much still yet to do. And the future of this community is is bright and good things are going to start happening because they've got people who are working towards a better community and you can't stop that kind of momentum.


Hi, everybody. Welcome for this new Jenkins inframitting. Today, to the agenda, we don't have many different topics. We just did the new weekly release of the version 2.280. I think everything went well. At least I did not see anybody complaining about that release yet. Just the thing that I want to highlight here is the weekly release. Yesterday, I was correctly notified when we had issues during the LTS release. I think that was LTS release. So that's realized that we can now detect if the release process was interrupted for some reason. The next topic, I think it's Mark, who brings this to the agenda, which is the fact that Microsoft won't officially support Azure plugin around 2024. From my point of view, it won't be a big deal, because the long-term goals is to rely on Kubernetes anyway. So we won't be using Azure container instances anyway. To me, that date seems quite far compared to today. I'm not worried about that. It doesn't change anything anyway. The last year, they've only been doing emergency fixes. Yeah, and it's not like nobody else can modify that code. So if, for instance, you compare that to Amazon, do not officially support the EC2 plugin, for instance. It's maintained by the community. So yeah, from my point of view, I'm not worried about that. But yeah, the main topic that I want to discuss today is about the CA certificate used to sign the update center. So, yeah.  We spent 12 months migrating JIRA. And ci.jenkins.io is a lot more complicated than JIRA. I don't think we need to do anything dramatically different, but I think we should remind ourselves that Azure is probably not, Azure in particular, ACI, is not our long-term destination. We really do, just as you said, long-term want to be on Kubernetes, and we want to be more portable than we are right now. So I think we're going to have to spend some effort to become more portable, and we just acknowledge we're going to keep spending that effort. So on that specific topic, Debian, who's not there right now, is looking at how to provision agent on Kubernetes. So we provision an Amazon cluster. And so we have ongoing work there. Nothing really major to report or highlight, but I mean... Super, Ben. So long as I don't want to arrive at 36 months from now and be surprised that something went wrong and we need to make a frantic move. So just planning is good enough for me. Thanks. So right now, we are planning to use Kubernetes to replace the Azure container instance. That's one of the plug-in. We could also use the same approach for the Oracle Cloud, whatever, Kubernetes-sponsored we have. We still have specific integration with Azure, but we don't have, I would say, strong requirements on the plugins. We still have some work around. So I mean, right now, they were just officially supporting those plugins, but yeah, we still have options and I'm not really concerned about those plugins anyway. I don't think they will stop working the day and date anyway. So I propose to continue to the CA certificates. So basically, inside Jenkins Core, we have a CA. So basically that CA is used by Jenkins to know if it can install. So let me explain this different way. So the update centers use a certificate to sign the package, the plugins that we want to install and that certificate is expiring. So the next time was something like one year ago, I generated a new one, but the problem is we use an old CA to sign that certificate and that old CA is expiring in April 2021, basically. So we need to now use a new CA that was introduced in Jenkins Core around April 2018. So basically, once we decide to use the new CA, it means that version older than 2.117 won't be able to download plugin from the update center. We delayed that decision several months ago because we didn't want to change that at that time, but I think it's time now to announce that. We will renew the, we will sign, we'll sign the update center using a newer CA, basically. I'm not sure if we can just send an email on the dev meeting list or if we have to send a blog post. I don't think it will impact the community because anyway, the version 2.117 is really old. So if the, I mean, for those people who are running that Jenkins version, they are not able to use the update center anyway. So any question on this? So you mentioned how old, what was the Jenkins version that will be the cutoff point? 2.117. And so the new, the new, the new root certificate, the root certificate is valid until 2028. So it gives us seven a year. Yeah. My sense is I think we should do a blog post just for deniability. That's a terrible thing to say, but that way we can point to something and say, look here it is, it was posted on the official site, but email to the dev list is the more likely thing it'll actually be read. Okay. I mean, I can send an email. I can send a blog post and that's, there is not a lot of things to say, just we are rotating the root CA and basically you shouldn't be affected by that, but yeah. Yeah, I don't know, blog post is really needed. That version is ancient. They're not gonna be able to use, so they won't be able to update plugins anyway. So it's basically impossible from the community update center anyway, because any plugin you try, the only plugins you better install are plugins with an old baseline that have no dependencies. This Jenkins core will always update to the latest version of a dependency. And if it's not using the LTS update center, which we only keep last four, it's just gonna break. It's, so it's basically impossible to be updating. So yeah, and I think I understand Tim yesterday or yesterday during Doc's office hours, we did a development exercise using a plugin and it defaulted to running 2.176 and immediately started offering plugin downloads that couldn't be used with that version. So you're right. So maybe it is pointless to talk about a blog post because it was already unworkable today. I think that's what you're saying, right? It's already unworkable today and a blog post isn't going to make it any less unworkable. So maybe we don't bother with a blog post and don't take Olivier's time writing a blog post, just the email to the dev list. Yeah. Okay, Olivier, are you okay with that? I'm persuaded by what Tim noted. Yeah, definitely, I mean, that's easy to just set the email, okay. Yeah. Okay, we don't have proposed to, is it already next week, the contributor? So yeah. It is, contributor summit is next, is 23rd, 24th and 25th. And actually we've got two voice, three voices that will be in that summit on this call that I wanted to check with. So this is a great excuse to ask some questions. Sure. Last topic, which is about the contributor summits, apparently it's next week. Right. So next Tuesday is the opening session of the contributor summit. It will be from three to five PM UTC. And in that we'll have five to seven minutes for each of the heads of special interest groups for each of the officers. So Tim, you'd have five to seven minutes on the presentation to share the progress from the last 12 months of release work and what you think should be coming. Olivier likewise, you can go less than that. Yes, seven minutes to just cover all the things that we did. I mean, it's not a lot. Well, not just all the things we did, all the things we did and the ideas you would like to propose for the coming year. And then we will organize ourselves into tracks. And one of the tracks I think is going to be securing the delivery pipeline for Jenkins components, for Jenkins plugins, et cetera. And there I think infra and release and security all should be involved in that single track. So first question, Olivier, I think you've already confirmed for me, you're willing to speak for a few minutes at the start. Tim, are you willing to speak as well as the release officer during that opening session? Yeah, yeah. Okay, then there was one more topic, which was on Google Summer of Code. And Kara, since you're here, would you be willing to speak on 2020's Google Summer of Code and on 2021's plan for Google Summer of Code? Yes. Thank you, Mark. The Google Summer of Code application as an org is wrapping up. And what we really need from you all, if you're interested is to put your names down as willing to be mentors for the different listed projects on the GSOC page. We have, I believe six of now, there are two more potential ones in the pipeline. One is almost certain to be end. So there is a bit of a choice. A lot of very interesting ones, Mark has put one forth. And there in addition are a number of really good ones on the cloud native topics, things like that. So if you are interested in being a mentor, you will not be the only mentor on any of these projects. You will always be prepared with another mentor. That is our goal. Ideally, we would even have up to three or more mentors. And this year's GSOC is requiring a reduced amount of hours from students, nearly half the hours. So it's only 175 hour projects over the 10 weeks. So that time will be divided up in different ways. And mentors will work with their students to determine what works best for the mentors and the students. But this means that students will be likely writing less code. I can't say that mentoring will be cut in half, but it will in all likelihood be quite reduced. What's required of you as a mentor, because what's required of the student is reduced. So hopefully no mentors will find the process entirely enjoyable and not onerous and not feel overwhelmed by it. We want to support you through the whole process. And I encourage you all to please volunteer as mentors. Thank you. All right, so proposal is to cancel next week's meeting in favor of contributor summit. Any objections? This sounds great. So I can start the event in the calendar. Great. That's all that I had, Olivier. Thanks. Thanks. Then I propose to stop the meeting here. There is no point to keep it for 30 minutes. So thanks for your time. And see you later. Bye-bye.


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OK, tako bitten, to je po verbenju, da v bistvu pomečenih tudi in zelo, zelo, ni ne bo SmartCraft, masli možemo pričvega kimi, zelo, arrike, tudi zelo, naredišno idemo nekih spojftakov, kot tako nekaj vsočim, ni odmah je odpovedal, kaj kaj bi se zelo, pa tudi se našel kako mi je popril, preseperatora algev we get is interesting by enumerating some examples, so I told you that the boring examples of freefield theories where we get some symplatic bosons obeying this kind of OP where in some representation representation R of some group G, those would be the half hyperths, and then we are going to have a b c c gos system, these are adjoint indices of the group, they correspond to the vector, and so you may think then to find the vertex operator algebra that corresponds to a Lagrangian n equal to 2 theory with group, gauge group G and R matter, I mean half hypermultimate representation R, you just need to take the tensor product of these two free vertex operator algebra and construct composite operator which are singlets under the action of G. That's of course a reasonable first guess, but upon further thinking it's clear that cannot be the right answer. So simply restricting to gauge singlets will generate some voa, let me call it zero, that clearly corresponds to the voa which is obtained just from starting from the free Lagrangian. If I switch off the gauge coupling, remember there is a gauge coupling tau and I switch off the gauge coupling, I literally will just find the tensor product of the free hypermultiplet and the free vector multiplet, and all that I have to do is to impose the Gauss law constraint which amounts to restricting to gauge singlets. So this is the correct answer in the free limit, but as I emphasize multiple times, the free limit corresponds to one of these singular casps, and it's boring because we have this just tensor product of free theories, we want to do something more interesting, and so we really want to describe the vertex operator algebra in the middle of this conformal manifold, and there are a first set of good news is that all you need to do is to consider the infinitesimal one loop correction to this result, and what that is going to do is to lift off a bunch of the operators that you have in this free approximation to the vertex operator algebra, by the mechanism that I quickly reviewed yesterday, several of these sure operators multiplet will combine together to form a long multiplet, which is then able to acquire an anomalous dimension as a move away from this free field point, and then away from the street zero coupling point, I should forget about those operators because they are not protected. And so the moment I move away in infinitesimal distance away, so as I turn on the coupling, or coupling on zero, there will be a smaller VOA, strictly smaller VOA, which is the one that I really truly want to identify with my interacting theory in the middle of the conformal manifold, and one can argue that this is sufficient to look at the infinitesimal tronkation of the operators, and moreover the other good news is that then any continuous deformation inside the conformal manifold, which is epsilon away from these casps, the vertex operator algebra is invariant under any such continuous deformation. In other terms, the state of space as well as all the OP coefficients are independent of exactly marginal couplings, the moment you are careful to take into account this continuous jump that happens at each of the casps. So in that sense, the vertex operator algebra associated with the 40-th theory captures, if I have a Lagrangian theory with a marginal coupling, this captures protected information, which is truly invariant under any deformations of the theory, including marginal couplings. And there is a very elegant, concise prescription to find this restriction of the naive VOA associated with the freefield theory, to the one interacting theory, which consists in the following. First of all, we are going to take this naive tensor product of VOAs, and the correct VOA will be obtained by, let me put it this way. We are going to compute a homology, a homological prescription, where there will be some differential, which I'm going to call QBRST. I hope the story is clear.  Now I'm purely in the two-dimensional world, and I assert that it's possible to take into account this continuous jump that happens away from the cusp by imposing that the states that remain are a subset of this naive tensor product, which is the homology classes of this operator, vcGhostSystemA. So let me explain a notation. Well, first of all, CA is clear. It's the ghost that corresponds to the four-dimensional gauge, you know, with a joint index A. And then by assumption, we know that the matter field transform in some representation are of the group that I'm gauging. And so I told you earlier that very generally, any time that you have a continuous global symmetry that induces that statement is sent to the fact that there is a affine, this is an affine cut smoothing current, which is purely made of Q and Q tilde. And in fact, given that Q and Q tilde have dimension one-half, you can instantly write it schematically. This would take the form Q, Q tilde, again, with the matrix of the representation of G in the representation R. And this is just the ghost current, which is made of BC. You can also write it down. It corresponds to the, again, to the same continuous transformation G, but now acting in the adjojn representation on the BC ghost themselves. And it turns out that this object is nilpotent precisely when the level of the matter current equals to minus two, the dual-coxet number of G. And if you translate in two-dimensional notation what I told you in the first lecture, this is precisely the condition for the vanishing of the four-dimensional beta function. So, if this gauging procedure is allowed in four-dimensional, meaning that it preserves conformality, then I can find nilpotent BRST operator purely written in terms of these two-dimensional data. And I'm claiming that pass to the homology of these BRST operator removes all the sure operator that recombine into long operators and leaves me with a truly protected operator in the middle of the conformal manifold. OK, so you will understand that then this gives a prescription, a very concrete prescription to calculate the VOA in all Lagrangian examples. And in fact, it's more general than that. If you have one of these mysterious building block, generalized matter theory that I talked about in the first lecture, and you know the VOA that corresponds to it, let me assume that I know it, and then I do a gauging procedure such that I gauge some subgroup of the global symmetry in such a way that this condition is obeyed, you see this condition is phrased in a purely universal fashion, that does not depend on having a Lagrangian description, then the exact same procedure will work, where now I will replace the free VOA for the symplatic bosons with this strongly coupled building block, which is the VOA of the generalized matter super conformal filter. OK, so this gives a powerful way to construct VOAs in many examples, although admittedly computing this homology can be a little complicated, and so what we often do, we come up with a, we do a level by level calculation starting from h equals small and then going up, we convince ourselves that we have a plausible guess for the VOA, and then we subject it to a variety of checks, and then formulate a conjecture, and then mathematicians prove it. That's a typical workflow in this kind of examples. OK, so let me now give you a few, let me give you a couple of simple Lagrangian examples, and then I will make a list of VOAs for several more non Lagrangian examples, where this kind of approach is not available, we cannot, this is in some sense, it's a preferably constructive approach. We know the free theory, we compute this very psychomology, maybe hard to compute it, but it's clear that there is an answer, that often you can guess. In the non Lagrangian case is more of a, again, a guesswork based on plausible assumptions. It's often the case that you know some data of this mysterious Lagrangian, you know, central charges, you know the global symmetry, you know a little bit of information about the Higgs branch, and put this information together, it's often the case that there's one compelling guess for the associative VOA, which you can then send subject to a variety of checks. OK, so let's do the simplest example in the Lagrangian word, which is this, we take g equal s u 2 and n f equal to 4, as I indicated yesterday, what you really should do is to think in terms of half hypermultiplets, which are in the so 8, so the naive flavor symmetry would be u 4, but it truly enhances to s o 8, and then the index a is the, this is the flavor, and this is the, this is the gauge group, and this is the four dimensional field, but without further ado, we have learned that that descents to a, to a simplect boson, and so the matter part of the theory gives me sympletic bosons that obey this OP, and then, and then I have B and C ghosts in the adjoint of s u 2. OK, so no, so you can do this exercise now, you can compute this comology, this exercise is actually not so easy, and what you discover is a rather elegant result, the result in voa, the voa of this s u 2 super q c d is nothing but the so 8 current algebra and level minus 2. I mean, of course, the level you could have computed instantly by using this formula, we know the level of the four dimensional flavor current, so we can just compute the level, and it's the other statement that I want to make, so you remember that the flavor currents are in the B-hat 1 multiplet, and we also know very well, because in Lagrangian theory we can, we can study this in without any problem, we also have detailed knowledge of the Higgs branch, in fact, I left that as an hazard size yesterday, did anybody do it? I will tell you the answer later, and I explained yesterday how one can describe on very general grounds, one can describe the Higgs branch of a four dimensional super conformal field theory as a hyper killer cone, it has to be a cone because as an action of the dilation symmetry, and for our purposes, I also explained that the best description is useful for us is to think of it as a simplatic, as a holomorphic, I explained this in the discussion section, perhaps not all of you were there, as a holomorphic, simplatic variety, which is a cone, almost simplatic cone, and then we can look at the, so this is hem Higgs, we can look at the halgibrolomorphic function of the Higgs branch, and we identified this with the Higgs chiral ring, which is generated by the Schur operator equal to 2r, so which is the ring of Schur operator equal to 2r, and I also explained that we can describe this ring in terms of a finite set of generator obe in some relations. So the generators of the Higgs branch are then in the language, in the four dimensional language, are then the highest weight of this behead, behead r multiplets, such that by taking products of them, I generate the entire set of operator obe this condition. Is this clear? So we have detailed knowledge, not just in this simple example, in many examples of the Higgs branch, as a variety, so we know the generator, we know the relations, we know the simplatic structure. In Lagrangian example, like this one, we can compute them by the hyperkeler quotient, and in non-Lagrangian examples knowledge of this Higgs branch data comes from more indirect consideration, maybe you can embed them in string theory, maybe you can get them by various duality, so we have, anyway, the Higgs branch data is very robust data, so it's something that we can often get either very directly by doing the hyperkeler quotient or indirectly by some other considerations. And the structural fact that I want to emphasize is the following little theorem, as you can prove using the construction I've given you so far, that generators of the Higgs branch, first of all they are Schur operators, so they must appear in the chiral algebra, but they are necessarily generators of the chiral algebra. Okay, so let me emphasize this little fact, which is important. The generators, the Higgs branch chiral ring, which is also the same thing as homomorphic function of the Higgs branch, under our map kind become what are called in the mathematical literature strong generators of the VOA, and let me, you have always known all your life what this generator is, but let me explain it to you, you know, all knowledge is reminiscence, as Plato said. So what is a generator, is the thing, if you, a VOA is uniquely characterized, if you find the generated VOA, which is the very large, which is pretty much any VOA you've ever seen in your life, is characterized by listing a finite set of operators, such that if you take normal order product of homomorphic derivative of them, you generate the entire set of operators. It's a bit of a mouthful, but it's, it's a triviality. Examples, Virazoro has a single generator, known as T of Z. All operators of the theory are obviously obtained by taking arbitrarily many products of T sprinkled with homomorphic derivative, clearly enough. For a fine cut smoothie is the, the generators are just the current, and then it's the same story. You're now gonna take arbitrarily many products of homomorphic derivative of the currents, and that is the entire state space of the VOA. You may be familiar with W algebras. For example, the vanilla type of, the vanilla type of Wn algebras will have generators T, which we also can call W2, W3 all the way up to Wn, which will have homomorphic dimensions 2, 3, up to N. And those taking normal order products of homomorphic derivative of them, you get the full state space, et cetera. Okay, so generators of the Higgs branch current ring become generators of the VOA. And of course we know that at the very least, okay, so perhaps I want to keep the suspense a little more, but, okay, let me, let me not give, I don't have time for this kind of, this kind of, of theatrics. So let me just give you the answer for what the Higgs branch of this theory is. The Higgs branch of, of SU2 super QCD. Okay, so let me write and then I'll explain it. It's the same thing as the closure of the minimal important orbit for SO8. And, okay, so that is playing the notation, it would take me a little too much time, but let me explain this in a concrete way. So this means that I take some formal generators x, let's call them xm, where m is an adjoint index of SO8. And I take the symmetric algebra of, of this complexity phi, the algebra of SO8. And I impose a single quadratic, a set of quadratic relations. So this object is in the adjoint of SO8. What are these objects? These are nothing but the moment maps. These are the dimension to, these, these, these are the things that correspond to the objects with e equal to 2 and r equal to 1. Right, the objects I have indicated earlier as mu. These are the objects which are the highest weights of, sorry, equal, the highest weight of SU2 which are thrown in the adjoint of the flavored symmetry SO8. Those are the ones that correspond, those are, those are elements of the Higgs branch, and the claims that they generate the, the full Higgs branch. But there is a relation that happens in the quadratic order. And the relations, so if I take a product of two such objects, given that critical mu, they are bosonic objects, I'm going to find, I have to take the, the symmetric product of the adjoint of SO8 and symmetrize. And the adjoint of SO8 is the 28, so, sorry, is it the 28? Sorry, it's the 8 times 7 divided by 2 is 28. Okay, yes, we're good.  That's just a fat. And so the quadratic, so let me call this whole set of operator, let me call it I2. With this definition, then I'm going to impose that x tensor x restricted to I2 vanishes. Okay, so this may not appear immediately intuitive, if you haven't seen it before, but it's a standard construction. Okay, it's a standard construction because it's extremely general. It generalizes to, to any lealgebra, and for any lealgebra you do the same thing, you take the adjoint of g, any simple lealgebra, the adjoint of g symmetrize, and you define this I2 ideal as the thing such that I2 plus the red sum of the representation whose dinking labels are twice the one of the adjoint gives me the symmetrize prior to the adjoint. You can do this very generally, and for SOA that's how it looks. Let's do another example. Let's take g to be SU2. Well, then the adjoint of SU2 is 3, what is 3 times 3? Symmetrized. The same thing is 9, and you will recall that 9 is equal to 1 plus 3 plus 5, right? The triplet is the anti-symmetrization, and, well, I hope I'm not saying anything. This is really elementary now. So the symmetric product of two triplets gives me the 1 plus the 5. The 5 is the object whose dinking labels are twice the dinking label of the adjoint. Clear enough? The dinking label of the adjoint is 1. The 5 is dinking label 2. In this case, this is what I would call I2. OK? And so this I2 can clearly define what any Lie algebra is. It's called the Joseph ideal. And if I take the symmetric algebra of the Lie algebra g and I impose that the I2 vanishes, I find the variety, which is the minimal delpotent orbit of the algebra, and has a very simple physical interpretation, this is the modular space of instantons of charge 1 for that symmetric group. The modular space of SOA instantons with charge 1 is described by this variety. And so this is something, in the case of super QCD, this is something that you can really check by hand by doing the hypercaler quotient. If you start with the description in terms of the Qs and you do the hypercaler quotient, you will find that this is the answer for the variety. OK. So where does this lead me? Well, I asserted, and it's easy provable, that generator of the Higgs branch kaj la ring are generator of the vertex operator algebra. And so I know for a fact that the vertex operator algebra at the very least must contain this SOA at a fine currents. And the nontrivial part of the statement I was making earlier, so I said earlier, so I know, I certainly know, that the full vertex operator algebra SU2 super QCD must at least contain SO8, and I can easily compute the level which is minus 2. And the nontrivial part of the statement is that it doesn't contain anything else. OK. So that comes from a complicated homological calculation. But if you didn't know, if all you knew is that this symmetry has favored symmetry SO8, a level minus 2 goes, well, what is the minimalistic guess I can make is this one? A minimalistic guess in this business often turn out to be correct. OK. Questions about this? Now, there is, sorry. Sorry, I have a question. Yes. So the fact that that vertex operator algebra saturates the central charge that you want is not enough to conclude that there is nothing else. OK. Great.  So you may have objected that for sure I know that there has to be at least an additional generator or an additional operator t. Remember, I had this whole story earlier. I explained that very generally we always have a t that descends from the artsymmetric current of the four-dimensional theory. And so there must be a t. But in this particular Kd, I simply identify t with the Sugavara stress tensor of the affine current algebra. The reason for it, and this is a nontrivial calculation you can do, you can compute the 2D central charge using the formula I gave you earlier. The 2D central charge uniquely fits in term of the C anomaly. And it also happens to be the case that this value is numerically equal to the Sugavara dimension, the Sugavara central charge is the dimension of g times k divided by k plus a check for in affine current symmetry level k. And it agrees. So we know that in this case we could try to get away without introducing a separate stress tensor. But it's still not a compelling argument, or at least not a complete argument, because if my VOA had been unitary, this would have been a good argument. You check saturation of Sugavara central charge and then you know that you're done. You cannot add additional stuff. But my VOA is not unitary, so how do I know? Perhaps I could add an additional stuff that contribute to some substantial additional operator, which is orthogonal to this one. The story is a little bit more involved. But the conclusion is correct, and that's what I'm going to explain next. One needs a more elaborate unitary argument based on four-dimension unitary that will indeed lead to the conclusion that if the two-dimensional, in the case you have an affine current algebra, if the central charge computed this way, agrees to the Sugavara central charge, then you know for a fact that the stress tensor is the Sugavara stress tensor. So, yes. Sorry. They appear, everything appears, pretty much. Any kind of reasonable symplatic variety, a symplatic cone can be obtained in this huge group of theories. Okay, so, before I do that, let me generalize the story to a nice little sequence of four-dimensional theories. So, these are names, let me also put H0. These are names that are associated to kodaira singularities. Not all of them, but some of them have these names. And if I consider an f-theory singularity, which you can think of some d7 nonperturbative d7 brain setup in type 2b, and I probe it with one d3 brain, the field theory that lives on d3 brain reduces the low energy to a superconformal field theory. So, this is a simple nice sequence of superconformal field theories that have one-dimensional Coulomb branch, because you have a single d3 brain. Okay, so this is, you know, appealing to the knowledge of those of you who know a little bit of these things. If you don't, I'm just take my statements.  All right, so remember that d3 brain can be understood as an instanton inside of the seven brain, and so the instanton moduli space of, so h0 is no flavored symmetry, h1 corresponds to flavored symmetry, su2, this is su3, and these are the obvious things, e6, e7, e8. I find superconformal field theories. Let me just name the superconformal field theories by the names of the associated kodaira singularity. These are rank 1 superconformal field theory, rank 1 because the Coulomb branch is dimension 1, with this amount of flavored symmetry. And the hex branch is the one instanton moduli space of gf. Okay, the case that I just studied, the Lagrangian case, is this one. In this case you don't need f theory, this is a perturbative. Something you can see in perturbative string theory, and so this is a case that has a weak coupling limit, and it's the example of superqcd su2 with four flavors. The other examples are non-perturbative. So with the exception of this theory that has no hex branch, the others have, the hex branch is the one instanton moduli space of the corresponding flavored symmetry groups. So that is a very nice simple generalization of the story here. What is the VOA? Well, it turns out that this one is the V erasoroalgebra at level minus 20, at central charge minus 22 over 5. This is su2, a level minus 4 thirds. This is su3, a level minus 3 half. This is the one that we just did. This is su8, a level minus 2. This is the 6 at a level minus 3, is 7 a level minus 4, and e8, a level, because you know it, but I wanted somebody to say minus 5. Okay, so how do we know this? Well, first of all, minimalistic guess. Again, we know that this must be subalgebras by the argument that I gave. We know the level, so at the very least, this is contained in the VOA, and the fact is, exalt the VOA requires further arguing. So now I'm trying to give further arguments for it by thinking a little bit in terms of the constraints of four-dimensional unit art. Okay, but before I do that, let me make the following.  Well, at the very least, you should be mildly impressed by the fact that if you believe this correspondence, I now get to compute a huge amount of correlation functions in, you know, coefficients, dimensions, et cetera, for some strongly coupled theories. A priori, you would not have had easy access to, because everything downstairs, these are just a fine casue of the algebra at some funny level, everything downstairs is perfectly computable, and so I can lift up that information and learn about this nice BPS set of the four-dimensional theory. And this is something that is actually really useful, because, for example, for this E6 theory, we use this information as input to fix a large set of data in the OP of four external operators, those we fix using this scalar algebra, and the unfixed stuff, which corresponds to long multiplets, we fed into this numerical booster machinery that I discovered in Michael Locchio. And then using that numerical booster machinery, we fixed, or more precisely put bounds, but we believe that they are saturated on the non-protected stuff. But this program couldn't really have got off the ground if we had not known this huge amount of protected information, because that was the only way to tell the boostrap that we are speaking about this particular theory with the E6 symmetry. Okay, so there's practical implications, but let's look at now and more structural properties, and let me go back to this grading that I had earlier. So a priori there's a third quantum number, little r, but I'm going to forget it, because in all of this example, all the operators have little r equal to zero, so it's not important. And remember, we also had this relation that little h was r plus l, from which, of course, we conclude that r is smaller or equal than little h. Or operators where r is equal to h, these are operators that in 40, these are Higgs branch chiral operators. So the subspace v11 is the space spanned by the affine currents ga. But if I want to think in terms of states, I put a vacuum here. H is equal to 1, and I also know for a fact that this descended from the BHET1 multiplet that had r equal to 1. Okay, so in this simple case, there is a clear assignment of little r. Is this clear? Little r could have been zero or one-half, but I'm assuring that that's an impossibility because there's no four-dimensional multiplet with those charge assignments. So we know for a fact, also more concretely, we know exactly where the affine current came from. It came from the four-dimensional moment map. So I have an ambiguous assignment of this r-quanton number. But now let me look at j minus 1a, j minus 1b, and things here are more tricky. Well, first of all, it's clear enough that the h assignment is 2. I just count 1 plus 1. But what is the r assignment? Well, the r assignment a priori can be 2, or it can be 1. Yes? I don't know the r assignment a priori. And it cannot be zero because this is not a thing that exists. But now I'm going to play a nice little game, and first of all, let's first consider the case in which we project these objects to some non-singlet representation is not the singlet. So what is v21? V21 is an operator with r-charge 1 and dimension 2. But let me claim that the only possible state with these quantum numbers is the stress tensor. The only multiplet in four-dimension, if I assume that I have a unique stress tensor and there are no higher spin concert current, blah, blah, blah, that will lead to this charge assignment, is the four-dimensional arc-symmetric current. But the stress tensor is clearly a singlet. So in the non-singlet sector, I know for a fact that this is v22. Why is that powerful? Because I gave you earlier a little rule for computation of the norms. So if I know r, I know h, and in this case, actually it's very easy to decide what sigma should be. Sigma contains a minus sign. That is the minus sign we saw earlier in the flip of the level. I now have an inequality to satisfy that I can impose on this gadget. And the inequality is actually non-trivial. I can compute the inner part of these j's just using the commutation relations in the affine-cats-mudic current. And I find that this inequality leads to a bound on k. K has to be smaller or equal than some number that depends on g, on the flavored symmetry. When this inequality is violated, I find a contradiction with four-dimensional unitary. And, well, happily enough, the bounds are precisely saturated by this sequence of algebras. So the bound for SOA tends to k has to be smaller or equal to minus 2. But how do we interpret saturation of the bound? The only way that I can have saturation of the bound is if this state is null. And so this actually means, and you can check, that SOA is a level minus 2 if you go ahead and compute the restriction of this gadget onto the 35v representation. This is null. And what does this mean? It means that the upstairs theory, the four-dimensional theory, must have a relation among the Higgs-Brand generators, which was one of the relations that defined the SOA minimally important orbit. And that, of course, everything hangs together. It's only at this particular level that I can hope to reproduce the four-dimensional Higgs-Brand, because it's only at that particular level that the multiplication of my affine current as an outstate, and then outstate seen as the presence of a Higgs-Brand relation. So there's a very nice interplay between the four-dimensional geometry and representation theory of these vertex operator algebra negative levels. And you will recall that that they, well, okay. So that's half of the story to get the correct Higgs-Brand. And the other half of this, sorry, this sets to zero really all these gadgets, 35v, 35s and 35c. To get the correct result, now I need to argue that the singlet, there's also a relation in the singlet in the Higgs-Brand. And that requires a little bit of further argument, because if I now project this representation on the singlets, of course, that's precisely the case where I can have a contamination of the stress tensor. So what we can conclude on general grounds is, so now let's do the non-singlet case, the singlet case, sorry. So if I take now this to be the singlet, in fact, let me precisely map it using the gilding form. This is what is sometimes called S. It's the unnormalized Sugavara stress tensor. Well, now it's trickier. So a priori this could be an object, which I'm going to call mu squared, which lives in v21, sorry v22, plus alpha times t, which lives in v21. Okay, so t is the map of the arcimetry current. Remember that story. And mu squared is what comes in the image of the product of mu, of the operator that I called mu before in four dimensions. Okay, this is a Higgs branch operator. It has, is in b hat 2, and it has r equal to 2. And this is something else. So a priori I have these two components. But now it's a trivial hazard size, again using the fact that I know all the discriminational relations in the V8 to actually compute alpha. Alpha turns out to be something like dg. Let me actually copy it to be precise. Turns out to be k divided times cg divided by c. And so actually here you truly have an overlay. You see, that's where this business of assignies are grading becomes interesting. You may have thought that naively, given this is the problem of two things with r equal to 1, has r equal to 2, but not, not really. It has a piece with r equal to 2 and a piece with r equal to 1, but I know exactly how they come about. And now with this sophisticated, more sophisticated knowledge, I can go ahead and impose positivity of the norms. And I'm going to discover that positivity of the morph imposes inequality on the, sorry, it's the other way around, inequality on the two-dimensional central charge that say two-dimensional central charge is greater or equal than the Sugavala central charge as a consequence of four-dimensional unitarity. And when it is saturated, it means that I have a null state and what it is null state is mu squared. When this inequality is saturated, the two-two component that corresponds to the square of the moment map in the single representation is set to zero, but that is of course precisely the missing relation, the missing quadratic relation that sets to zero, the product of the SOA moment maps in the single representation. And so lo and behold precisely when these bounds are saturated, we can conclude that we correctly reproduce the four-dimensional Higgs branch and we're happy. Okay, so the story becomes very rich with these unitarity bounds because you see, here I was using very special properties of this very universal type of operators, but the moment I go to level three or to level four, I don't have that in my disposal and then the game becomes a lot more intricate, but nevertheless with more work you can play it and it leads to sort of very interesting conclusions. For example, one relatively easy thing to establish is a universal bound on C. By playing a similar unitarity game you find that there's universal bound on C alone. C to D is molar or equal to minus 22 over 5. This translates into a statement that C for D is greater or equal to 1130 and sorry, this assumes that there are no higher spin conserve currents. So you got a very cool result, that the four-dimensional central charge in a interacting four-dimensional theory has to be bigger than this number. When you have this number, it means that the corresponding Verozoro algeva in 2D is precise, the Verozoro algeva of the Li Young minimal molar, which is the 2.5 minimal molar. And so it's rather surprising you get to put a bound on the simplest interacting four-dimensional super conformal field theory. But then you can get going and using a more elaborate reasoning, which again amounts to careful examination of these graded spaces and norms, et cetera. We haven't finished it, but we are pretty confident about the following little hope for theorem. That the constraints of 4D unitarity and plus additional boost of consent that I don't have time to discuss. Using this, and if I up to now everything was complete universal, I had to make no additional assumptions about what further the vertex superalgeva could contain apart from these universal subalgebras. But if I further assume that the entire kala algeva is just Verozoro, this is a strong assumption, of course. If I assume that the entire kala algeva is just Verozoro in some central chart C, then I get to make stronger statements, because level by level I know that the entire space must be made of Verozoro and then imposing orthogonality is rather stringent. And then you show that the only allowed values of C are the ones that correspond to the 2,2M plus 1 Verozoro minimal models. Any other value would lead to a negative norm in four dimensions. Okay, so this is the beginning, hopefully, these baby steps into a classification program. So the main lesson here is that the kind of vertex operatoralgeva we get by this 4D to the map are very special. I illustrated in some example that truly are very special. You get very specific negative levels where you have a ton of null states, which are needed to reproduce the four-dimensional geometry. And they are special really because if you are away from these very specific fine-tuned levels, you are in danger of violating the constraints of four-dimensional unitarity. So if one could really characterize and axiomatize the property, the additional properties VOA must have in order to be same from four dimension, you could perhaps hope that this is the beginning of a classification program of at least those VOAs. Now the question of whether two different 4D theories could map to the same VOAs, of course, open, but there are no counter examples at the moment. How am I doing with time? Like zero minutes. Zero? No, how much time do we need?  I can go on forever or stop now, but... And we can summarize sort of the big picture. So I at least give you a glimpse of how four-dimensional unitarity enter the story and how one can reconstruct the geometry of the four-dimensional theory from this representation theory of the VOA. Let me mention one last thing. So clearly the VOA has a lot to do with the Higgs branch, but it contains more information. And so this is part of our ongoing effort is to try to characterize precisely which additional information, apart from the Higgs branch, you need to reconstruct the VOA. That's one direction. And a simple first step in that direction is if I hand to you the VOA abstractly defined in terms of a set of generator and their singularity coefficients, can you reconstruct the four-dimensional Higgs branch? This is a rather non-trivial question because the Higgs branch is there, but it's clearly somewhat hidden. The reason it's hidden is precisely this funny business of this R-grading. The Higgs operators are these ones. But I impress upon you that precisely extracting the leading term where they want to have H equal to R is in general non-trivial. If you had knowledge of this quantum number assignment then you could do it instantly, but in general you don't have. And the Sugavara construction is already the simplest of infinitely many such ambiguities that can occur. And in all examples that we bother to look at, there is a very interesting and very universal way to recover the Higgs branch. And I'm going to end with that. So it's still conjectural, but surely true.  And I'm going to spring this in a minute, but the compelling conjecture that we have is that this is nothing but the Higgs branch. Okay, so how do we construct this variety? So let's assume that the VOA is given by some set of generators. I gave example before, some finite set. Then we can consider polynomials in the formal variables as we, we drop the Z dependence and we consider polynomials in formal variables, one variable for each generator. So example, in the case of Virazoro, we would just consider polynomial in a single variable t. And then we mod out by relations which are obtained by the presence of null states. Let me give an example. Let's do the Virazoro minimal model at of 2,5. Then you will remember that this, I don't remember the coefficient by heart, but there is a null state of this form in this theory.  But L minus 4 is twice the derivative of t. And the idea that I'm dropping the Z dependence really means I'm working modular derivatives. So I actually want to throw away derivatives which means that I should really set that I should really consider polynomials in t modded out by the relation that t square is 0. Okay? That's, and you can generalize this game. You consider the nulls and you look at relations of this type induced by the fact that the null can contain derivatives of the generators. And you set those to 0. Now, of course, this is not a geometric space because it's just a fatten point. It's just t square is 0. And so the associative variety is then this space here further divided by nullpotence. Is the construction clear? I sketch it here. So in this particular case, if I further divide by nullpotence, I'm left with nothing. In other terms, the associative variety is a point. And that nicely nicely agrees with the fact that the Higgs branch of this H0 theory is trivial. There's no Higgs branch. And you can keep going. Check this story in all this example. It always works in this example and many more. But let me end with that sentence. Hopefully it will inspire some of you. This state, so I always universally have the same state. So I always universally have the stress tensor, because it always comes from the arc current. But if this conjecture is correct, you know, the stress tensor is clearly not the Higgs branch generator, it is the arc current. So it means, if this conjecture is correct, that there always must be an outstate of the form nth power of the stress tensor is equal to a holomorphic derivative of something else, which means that in this quotient the stress tensor must be nilpotent. And the existence of such an outstate allows me to compute the torus partition function by inserting this outstate and turning the statement that the insertion of this outstate should equal to zero into a modular differential equation that should be obeyed by the torus partition function. And so we get the rather curious statement that the vacuum character of this carnal algebra must obey a modularly covariant differential equation. In fact, we have discovered that this is universally true. These are vector-valid modular forms where the other solutions correspond to non-trivial modules of the VOA. And so this is very much still ongoing work. The physical interpretation of this modularity and this over additional representation which presumably correspond to the insertion of surface defects in the transverse plane is very much. Ongoing work. In fact, there was a paper today by the Dushensko and Fluder. I'll stop here.


This is stock number 11061. We are here at Summit Automotive in Fond du Lac, Wisconsin, you're new and used. Heavy-duty truck headquarters, today we are checking out this super clean 2019 Chevy Silverado 3500 crew cab, short box, single rear wheel. This truck has the 6.6 liter Duramax diesel with the L5P motor, which gives you 445 horsepower. This truck has been fully safety to and inspected by our service shop has a fresh oil and filter change. All the fluids have been checked and topped off and this truck is 100% ready to go. Cajun Red Metallic is the color we shoot all of our videos in 1080p, 60 frames per second so if you have HD capabilities on your computer, tablet or smartphone device turn them on right now because it is definitely your best way to check out the quality and condition of the vehicle before seeing it in person. If you'd like to check out all the photos on this truck in the upper right hand part of your screen as they link right to our website, click that and check us out there. Comes with the Michelin LT265 70R18 tires with these 18 inch chromed alloy rims. These tires look like they have probably about 50 to 60% of the tread left. Has the Z71 off-road suspension, frame and underbody looks very clean, driver's side front fender, no dents or dings on that. Has the projector headlamps, the factory fog lights front bumper is absolutely perfect. No dents or dings on that. The lower valence looks really good. The hood is in excellent shape as well, you do get that cowl there. They started that with the L5P. Passenger side front fender, no dents or dings on that. And the passenger side rim, no scuffs or scrapes on there. As you go down this side of the truck, take note of how clean the body is, how reflective and mirror-like that paint is. We take these HD videos so if you are far away or even if you're close by and just cannot make the trip down but you're still interested in purchasing the vehicle, you can see the vehicle, hear the vehicle and have confidence in what you're looking at before you even get here so that when you do get here there's absolutely no surprises. Cab looks really good. And that's why we offer the Summit Auto Fastpass option in the upper right hand part of your screen and link right to our website where you can apply for financing, get pre-approved, see a payment quote, even appraise a trade-off when you come for your own home. So when you get here all you gotta do is drive the truck, love it and you'll be all set to go. Frame and underbody, exceptionally clean, has all the remaining factory exhaust so it hasn't been altered in any way and it does have those nice chrome step bars on there as well.  Back rim, no scuffs or scrapes on there and as we come around the back of the box here looks good, rear bumper, no major dents or dings on there, full towing package which includes a receiver hitch four pin and seven pin wiring it also has the fifth wheel and gooseneck prep package in there. And the only thing I really saw in the entire truck is one tiny little ding on the tailgate here but it is a used truck. Has the shock down assist, spring and bed liner, gooseneck and fifth wheel prep and it also has the LED bed lighting up there, seven pin wiring as well. That factory soft tonneau cover is in nice shape as well, no rips or tears on that. Tailgate shuts nice and solidly and as you go down the driver's side just as clean as that passenger side, no dents or dings on that box for full disclosure this back rim is in excellent shape as well and down the rest of this side of the truck looks really really good. You get the telescopic tow mirrors, LED side lights, directional signals in the mirrors, they also telescope out like that and they are a manual fold in so they fold in like so. Inside the LT1 package gives you the black leather interior, power driver seat, factory all-weather floor mats, you do get auto headlamps, turned dial four wheel drive, factory brake controller, tilt and telescopic steering wheel, power windows, power locks, power mirrors, you got this kind of carbon fiber door trim going on there. And as we hop inside the truck, you can see that this one has 30,815 miles. You get the Z71 instrument cluster, looks really good. Leather wrap steering wheel, no scuffs or scrapes on that, bluetooth and information center controls on the right, cruise controls on the left and it does have audio controls on the back of the steering wheel. You get the allison six speed transmission with the optional tap shift, the Chevy MyLink system, AM, FM and Sirius XM radio capabilities on this radio. This is also where your backup camera is going to show up and this one has the projection so if you got Android Auto or Apple CarPlay on your phone, you can project your cell phone to the screen via USB and then if you've got a navigation system on your phone such as Waze or Google Maps, you can project it right to the screen and then it's like you have the navigation right on your screen but with a navigation system that you're more familiar with. Anyways, has all that and you got a CD player there as well. Heated seat buttons, dual climate control, stability control, cargo lamps, that's how you turn those LED side lights on, on the mirrors. Downhill assist control, factory exhaust brake, you do get a 12 volt power point and then you also have, if I can get under here, 115 volt or 110 volt, 150 watt plug-in down there as well. All weather floor mat on that side and carpeting is absolutely perfect, smells very clean in this truck, it's never been smoked in, passenger seat is absolutely perfect and the headliner is extremely clean, no rips or tears on that. You do get map lights up here and on-star and SOS capabilities in that rear view mirror. We'll take a quick look at the back seats and then we'll check out under the hood. The back seats are just as clean as the front seats, no rips or tears back here.  The fixed glass rear window with the built-in rear defrost, you do get a winter front on here as well and the carpeting is nice and clean and you get those all-weather floor mats back here too. All the doors look really good, bottoms of the doors of course look really good as well as do the kick panels and you can see those LED side lights extremely bright and those are nice if it's dark out and you got to see something alongside the truck. Anyways we'll take a quick look under the hood, I would personally like to thank you for checking out the video today and hopefully from this HD video you will have been able to tell just how clean this truck is all the way around inside, no under the hood we have the 6.6 liter Duramax diesel with the L5P boner, 445 horsepower engine maze very clean runs very smooth, this truck has been fully safety to and inspected by our service shop has a fresh oil and filter change, all the fluids have been checked and topped off, the truck has been gone through mechanically 100% and is 100% ready to go and to see more pictures of this truck or one of our other 450 new and used cars, trucks, SUVs, minivans, Wranglers, you name it we got it, go to that website right above the truck there, summitauto.com, full pictures and descriptions of over 450 vehicles from two locations all at summitauto.com and if you'd like to check out more HD videos you can go to youtube.com slash summitauto, remember to like subscribe and share on this video and all the videos that you see there in fact in a second you'll see a link to subscribe to our YouTube channel on your left a link to more Chevy 3500 truck videos like this one on your right if you have not been to our website on the bottom link to this vehicle on our website click those check us out and we really look forward to helping with this super clean 2019 Chevy 3500 crew cab short box LT1 Z71 in Cajun Red Metallic, thanks again.