Hello people of the internet, my name is Johnny and welcome back to another FNAF era video. Oh boy am I excited to be here today and I'm sure you guys know why I'm just so excited to be here. Uh let's see who the new character is because if you guys remember they promised four new characters they never once mentioned skins in their post about October so we shouldn't be getting a skin just saying because they did say four new animatronics they're getting multiple characters they never mentioned skins so I'm excited to see who the character is let's have a look oh toy chica that's weird I swear we've had to chica before um who knows maybe it's toy chica from ultimate custom night let's have a look boys um oh nope it's a skin okay let me let me talk about this for a second because I know a lot of people are going to be upset that I'm making fun of the skin let me get this straight I fucking love the skin in fact it's probably one of my favorites it just looks so damn good and I love the fact that they are representing um non-American cultures like this is for if you don't know it's for the day of the dead which I believe is a Mexican thing if I remember correctly um to celebrate All Saints Day or All Souls Day which is November 1st um so actually the reason why it is for the Halloween event is because Halloween is short actually for All Hallows Eve which is another name for All Saints Day aka All Souls Day it has a lot of nicknames but us Americans we usually celebrate Halloween um again October 31st the day before All Saints Day instead of All Saints Day um but other cultures do celebrate it so I'm glad that they are representing other cultures but and I mentioned this at the start that they never mentioned skins right I'll put the post up right now they never once mentioned skins they said four new animatronics and I know I swear that they chose their words very carefully there because an animatronic is it could be either a character or a skin both or animatronics so that you know they chose their words carefully there um and then they go on to say multiple characters not how many characters just multiple ones which um apparently we're getting three we are getting one next week so why are they throwing a skin this week I don't fucking know so yes I am upset that we have a skin I'm not upset about the skin itself I think it looks so damn good I hope I get it suit actually because again I feel I think it looks very very awesome I am I'm excited to fight her because I think I remember Torchig's mechanic um steroid her winter hairline with the mask on and then is that it I think I think it is because I know toy Bonnie's the opposite he's like springtrap with the mask um so I'm pretty sure I know Torchig's mechanic I will say I don't think I'm going to buy extra lows because I want to save them for the new character you know so let's find our Katrina skin where she here she is again I fucking love the skin it looks so goddamn good I'm just so upset oh thank you that it's a skin you know so here she is oh let's have a look at the animation oh looks pretty sexy if you ask me um god dang Lumix just saying that that animation is very suggestive all right so here is toy chica um okay I'm pretty sure I know her mechanic so she's over here and apparently toy I mean not jackal Bonnie not having sound was a bug okay sure um apparently he has sound now I don't think I've faced him since they fixed the sound so I can't confirm if that is real or not are you gonna talk to me at all because Torchiga does have a voice uh I'm not getting any voice line surprisingly oh hello very fast I wear I mean George there's a voice line there we go oh hello long haywire oh sorry yeah um so it's just the same as normal Torchiga because it is a skin no different CPU that is the definition of characters animatronics with a CPU or characters animatronics without a CPU or skins hello okay where are you you see her since she has a very fast George I'm gonna use the flashlight a bit even though I don't normally use it it's gonna be very hard to catch her okay actually maybe it's not that bad I don't know oh my god got lucky with that one if I lose I'm gonna buy some lows but if I win I probably won't because again I want to save it for the actual character next week which who it is I don't fucking know honestly I'm hoping nightmare young or nightmare mango don't know why I said nightmare young like that it's gotta be one of those two right maybe grim foxy maybe dreadbear doubt it though honestly since technically those boys are owned by the hell okay where are you owned by steer wool this is a long fight oh hello okay so here where are you should be yep got it hey look it's the other Torchiga skin by the way the merch for FNAF or should be shipping hopefully soon I honestly don't know when it's shipping you know man I just want to get this final voice gotcha gotcha gotcha oh nearly messed that up okay so you actually do have time to quickly put down the mask okay so that's actually good to know I thought she was a lot harsher than Chexley hello right over here oh jesus oh my jesus i like the new shelf by the way boys i move some things around six a.m board game vid coming probably tomorrow to be pouch out come on man just charge boom that lag though look the cupcake it looks so goddamn good oh what's going on why does my menu look like that ports remnant nope no no suit boys how unfortunate so I talked about this for like 10 minutes um in a earlier recording I literally sat down and I talked for like 10 minutes about how upset I am that Illumix lied to us again because I mean they did that um but I just want to quickly go over my um my thoughts on this again I am happy that we are getting a final character next week I think that's really going to make up for this week which again I do not think is a good week because they never said skins I actually have the posts up right now talking about the October update and they say for now just know that there will be multiple characters coming which we did get multiple characters and then in the next update post they said four new animatronics again they chose the award animatronics for a reason because one of the animatronics is not a character multiple characters will be released in October we are getting three but the way you awarded it makes people believe that we are getting four new animatronics and now I know people are going to be like oh too bad we got one skin out of four animatronics like that's not bad and I know it's not I'm just upset that they lied like I'd rather be I'd be so much more happy if they said you're getting four characters and a skin I would have been more fine with that I would have still been a little upset um not in line but if they just straight up said four new animatronics coming as we said in our previous September update multiple characters will be released in October there will be three new characters and one new skin I would have been fine with that but but they they made it seem like we were getting four new characters which we're not we're only getting three which again I know that's not bad odds three for one that's not bad at all I'm just saying I wish they were more honest and I wish they responded to criticism if you look on their reddit page the only comments that they reply to are comments praising their game saying that their skin or character looks fantastic and that they were so excited for this character when there are so many people out there that are like hey my game still crashes whenever I try to go into a fight hey my game still freezes at 90% somehow that's still a thing after months of being in the game I really do appreciate the hard work that Illumix does I'm just saying shut up I'm just saying that the way they handle the game and the way that they tease things is very misleading right the dark circus event that is a perfect example you know we were all speculating it's gonna be the fun time animatronics I wish they just straight up said after we were all speculating that it's the fun time characters I wish they just came out and said it's gonna be some skins right you're getting one character and you're getting I believe it was three skins I wish they did that and I wish they did the same for this October update I just wish that they were more honest really tell us what we're getting I don't care that it spoils the surprise I'd rather be spoiled than disappointed just saying anyways I'm not gonna look forward editing this because I always never like editing granting videos because I know people aren't gonna like me but honestly I don't care anymore uh yeah so that's gonna be it I guess we'll see you next week for hopefully a good character all right see ya Gregory be still I think she's found us


One of the biggest country icons, you might guess, the Dolly Parton calls Tennessee home, and you'd be right. While the singer has an estimated net worth of around $600 million, she still lives in the same estate in the Brentwood area of Nashville, which she bought back in 1999, $400,000. She shares the stunning farm-like property with her husband, Carl Dean, and the home's interiors certainly reflect Dolly's colorful and cheery personality, which she's so well-known for. Despite the fact that the home cost under a million dollars, the sprawling property doesn't lack in luxury amenities and updates, no wonder.


There she is. Publix, food, and armies. Yes. Welcome to Vlogmas Day 20. We are at Publix getting some food and we might make something interesting for dinner. Maybe not. We don't know. The brother is still missing. Yeah. The brother is still missing in action. He has decided to be lazy and not to come back when he said he was going to. So maybe he'll be back for dinner. We don't know. So anyway. Publix. Because this one wants peanut M&M's that are the red and green for the holidays. It's gotta be Christmasy. It's gotta be the holiday situation. But the issue is the grocery store didn't have them. They just had the regular ones and that's just not good enough. Nope. So we're at Target plus we need to get gift cards anyway so whatever. Maybe I'll do a Target haul when we get back. All right. So here is what we got at Target. Got a little holiday bag for this gift. This is for my cousin's kid Alex. Got a little waffle weave top and some gray cargo pants. My mom decided to get this from Marona. It's really cute. It's got like three quarter length sleeves. It's kind of sheer but it's really nice. I think she might wear it at one of her church outings, right? Yeah. Got a card and then some gift cards for Christmas Eve and then this is for somebody named Jackson and got some fun things. This is actually for possible Santa pictures next year but they were super cute and some of it was on clearance. So got a hat because you know you have to have that. And then this is really cute. Has like the little like Sherpa lining in there and this was on clearance and then these pants. Look at those. They're so freaking cute.  They're so cute. They're like all these nice flannel lining. Yes. And then the main reason we went finally got her her M&Ms found the peanut M&Ms that have the holiday colors. So yeah update brother is still not home and I think I am going to sit right here and I'm gonna work. So I almost forgot to mention this on the vlog but today is actually an interesting day. It is my parents anniversary day. They're both sitting here and nothing's happening. They're not even excited. So it's been what 42 years is that right 42 years of marriage. I just wow just wow. So let's interview them and see what it takes for 42 years of marriage to stay alive. What do you think mom? Patience. Patience. Patience. Okay. Dad what do you think? I don't think that's what made it work for me. Well there you go. So she's always right. I don't know about that. I know she talks sometimes it makes that noise with her mouth. Nothing else makes it work? It's a work in progress. It's a great plan so I just need a plan. Even after 42 years still work in progress. That's good though. They know we're yet. No I think I don't know if I'd be alive if I was single if the pain keeps me alive. Geez. You can be stimulated. It's a stimulated. I always tell me the best thing that ever happened to you. That's it. I tell it I always say that when she's with me. What happens when she's not with you?   Yeah we just you know it's just been a dream. It has. Mmm. My parents are weird. They're really nightmares. I mean otherwise. But I have nightmares. I don't have dreams anymore. My parents are obviously weird you guys. I apologize for any footage before this but apparently that's what it takes to have a 42 year marriage. Good luck to everybody out there by taking advice from my parents. I sent you the text. He's sitting right there. Yeah it's good. It helps me communicate. Digital family. Because of the proximity of such. Yeah. Dad says hi I'm on the couch next to you. Is that what it really says? I don't really know it. Oh my gosh. I saw my partner try to turn the fan off. It says hi. What does it say? There's what? You can't even human. What's going on? Speak louder for the camera Phil. It says don't tell Bob and Emily I just farted. Oh great. I see a swirly thing. That moves the fart that way. Same. That's why I'm sitting here. That's so helpful. So helpful this family of mine. There's like six dots of different colors. I'm sitting here trying to start talking in the vlog but it's not working out. My brother's back. Tell him I'm going to show him a picture. What does it say? Oh jeez. Really? With the googly eyes. Googles. It makes you almost want an earthquake to happen so you can watch the googly eyes. Oh gosh. My brother and I were just talking about possibly doing a video together. Like a standard sit down video and wondering if you guys have any questions for him. We could do like a brother sister tag or a brother tag. I don't know. I've done one with my mom and my dad a long time ago. If you want to go back on the channel and look for it, feel free. I don't know what you guys would want to know about him. I'm sure you guys have really good questions. And he's right there. You're going to say hello? It's tiny feet so don't ask. Seriously. This is the kind of stuff I have to deal with all the time. Thank God we live really far away from each other. A kid. A kid. Anyway. If you have questions, post them down below. I might also ask on Instagram if you guys have questions for him. Or you know, if I don't get a lot of questions we might just do like a standard tag video or something too. So anyway. Got questions? Leave them below. Why? Why? It's so dark. Whoa. Over exposed Emily. Ugh. Weird lighting again. I don't have my ring light with me but whatever. We're just going to go with it. So anyway. I'm going to close out the vlog here. I hope you guys enjoyed a little peek into my day. Really we just ran errands today. So sorry it wasn't that exciting. But tomorrow we're actually going to be doing something really fun. And we're going to go see some manatees. So I hope they are out. Hoping, hoping, hoping. So yeah. But if you have questions for my brother put them down below. And we will film some sort of video for you guys. I'm just not sure what that video is going to be. But anyway. That is a wrap on vlog 20. And I will see you later. Bye. That's going in the vlog.


I'm going to be talking about a project that has been going on for a ridiculously long time. I should mention it makes use of discoveries by many other people, some of whom are in the room. And at the appropriate times, I'll try to mention them. But if I forget, I think it will be obvious. OK. So I'll be sketching a proposal, a proposed mechanism that produces quantum field theory in spacetime, a real quantum field theory, a measure on spacetime fields, which is equivalent to a Hamiltonian. And at the same time, produces a quantum string background. And I'm reasonably confident that it's the correct idea of a quantum string background. But as things stand, that's a purely formal question. Whether this is how actual quantum field theory is produced, by which I mean the one that describes the real world, that I don't know. But I would like to. So at the moment, I'm trying to derive from this proposal a predictions of unexpected low energy phenomena that might actually be seen or not seen in experiments. And more explicitly, the possibility that this mechanism produces some, you'll see, rather bizarre low energy degrees of freedom whenever there's SU2 gauging variance. And these will be associated with a well-known, non-trivial homotopy group of the space of SU2 gauge fields on Euclidean spacetime. I get this too. OK, this is I should put in this caveat. This is extremely speculative, fundamental physics, a long shot. I like that word. It comes from when the British were shooting at the French. All right, it goes back, as I said, a very long time, the beginnings. So it goes back to this two-dimensional generalized nonlinear model where doing two-dimensional quantum field theory, the field lies in some manifold M. And the action is given by what mathematicians call the energy functional. The parameters in the action are comprised in a Romanian metric on the target manifold M. And this is a renormalized. So there are infinitely many coupling constants, which you can think of as the Taylor series of the metric at some point x0 in M. Then you get the metric. It's first derivative, second ad infinitum, infinitely many couplings. But they are all renormalizable. And the renormalization can be done co-variantly with respect to the target manifold. And the renormalization group equation has an expansion in the inverse size of the target manifold, which starts with the Ricci tensor. So this work was inspired by Sasha Polyakov's discovery that the two-dimensional nonlinear signal model is renormalizable, where the target manifold there is the two-sphere with O3 symmetry, the round two-sphere. So the only coupling constant is the inverse size of the two-sphere. And Sasha discovered that that was a asymptotically free coupling constant. So this can be thought of as a generalization of that. So what the renormalization, I was a graduate student at the time. And Ken Wilson's view of the renormalization group was how I learned renormalization. And one thinks of the renormalization group as a machine that acts on quantum field theories, in this case two-dimensional quantum field theories, and drives them to something new at larger and larger distances. So here, the two-dimensional renormalization group, and it's doing this at very short distances, it drives this metric on the manifold M towards a fixed point, which would be then a solution of reaching tensor equals 0. So the two-dimensional renormalization group is a mechanism that produces what looks like a classical field theory. Now, by mechanism, I'm not talking about a mechanism that acts in real time. It's an abstract mechanism that acts on theories. OK, so at the time, that was extremely exciting, though I think only to me. It seemed to me that it could be a clue to where the laws of physics come from. It looked like Einstein's equation, not exactly, but it looked like it. OK, so the questions that arose were, first of all, it isn't Einstein's equation. It's a field equation, but not a physical one. So the question was, is there something related that would produce a realistic field theory? By which, I mean, it should come from an action principle, and it should have a realistic collection of fields, not just a metric on spacetime. I forgot to mention that for this picture, one takes the target manifold M to be spacetime. So it should have gauge fields, fermion fields, scalar fields. Then there's the question. I was a bit sloppy when I said that the renormalization group drives you to a fixed point. Well, it only does that if that fixed point is an attractor. If that fixed point has unstable directions, then you have to do some tuning to get driven there. And at the time, I didn't see, I mean, you can eliminate all but a finite number of directions, but I couldn't see how to get rid of the possibility of a finite number of unstable directions. So how do you get stability in this sort of scheme? And then the big question, what this produces is a classical field theory. Where does quantum field theory come from? What makes quantum field theory? So within a few years, the first two were answered when this two-dimensional field theory was interpreted as the string background. So the idea is that the world's surface of a string propagating in spacetime is described by a two-dimensional field theory. And if the spacetime has a curved metric, the two-dimensional field theory will be this two-dimensional nonlinear model. And the condition that the beta function vanished, that you'd be at a fixed point, is a consistency condition. To get the verisoral algebra and thereby a unitary S matrix from this two-dimensional construction of the string S matrix. OK, so I can't possibly mention all the names involved in that picture of string theory, but I would like to mention my late colleague Claude Lovelace, who made the really remarkable discovery that string theory to be consistent requires the spacetime dimension to be a certain number, 26 for the Bosonic string. So that was, I think, the first example of properties of spacetime being determined by consistency conditions of string theory. OK, so it was realized that this condition beta equals 0 would be a physical field equation coming from an action principle. If you added, in addition to the target metric, additional couplings in the two-dimensional theory, this was Friedkin and Saitlin, who introduced, I think, what's called a dilaton coupling. And then, if one goes to the fermionic string, where you add fermionic two-dimensional degrees of freedom to get two-dimensional supersymmetry, you get more renormalizable couplings in this two-dimensional theory. Besides the metric and the dilaton, you can cook things up so you get spacetime gauge fields, fermion fields, scalars. And of course, two of the main people responsible for the fermionic string are in the room, Andre and John. In the fermionic string, the two-dimensional version of that stability turns out to be basically given by the GSO projection, which gets rid of tachyons. Tachyons correspond to relevant directions under the renormalization group flow. So you're getting rid of the main source of relevant directions. And then a complication, which I didn't point to. The Ricci tensor can have marginal directions. It can have a manifold of solutions Ricci equals 0. The higher-order terms in the beta function, curvature squared and so on, can produce non-trivial flow on that manifold of solutions of Ricci equals 0. And that can produce instabilities. So there was a remarkable discovery by Alvarez, Goumet and Friedman that at higher-orders, if the two-dimensional theory has an additional supersymmetry, these higher-loop terms cancel. And they discovered that the two-loop term cancels. And then later it was done to all orders. OK, so now we have additional questions. It doesn't seem right that the string background should be given by a classical field. You would think that the string background, the environment in which strings scatter should be a quantum state of the laboratory where you're doing a string experiment, or a hypothetical string scattering experiment. So the additional question is, what is the quantum string background? And then is there a mechanism that produces a quantum field theory in spacetime? So the classical background, the beta, the renormalization group flow, the 2D renormalization group flow, is producing a solution of beta equals 0. It's producing a string background. And the question is, is there a generalization that would produce a quantum string background? Well, I mean, you are getting the equations of motion by better functioning 1 to 0 for spacetime, so it's classical, but by default. You are getting not the Lagrangian in spacetime, but rather the classical equation. It's a long way from classical equation to go to Lagrangian. What I mean is that this beta equal to 0 is an equation of motion. Yeah, we have found it to be classical. Yeah. That's sort of the motivation for these questions. One would like to go beyond that. I don't know. This is probably personal. I feel an urgent need for a mechanism that produces quantum field theory. And there are too many self-consistent quantum field theories. If we're too much in the position of sort of groping in this huge space of possible quantum field theories, the world is described by one. So a mechanism that produces quantum field theory seems like it might give some explanatory power beyond there being just quantum field theory. So after quite a while, I came up with a proposal. So abstract a little bit. Write lambda i for the two-dimensional coupling constants. So lambda i are the modes of whatever spacetime fields describe the two-dimensional field theory. By modes, I mean the momentum modes in spacetime. And then let, I don't know what's that called, Cal-M in latex, be the manifold of spacetime fields. So the lambda i are coordinates on this manifold. Equivalently, we can think of it as since this is the most general quantum field theory in at least some neighborhood of a certain class of quantum field theories, we can think of M as the manifold of 2D quantum field theories. So to be slightly more concrete, each lambda i couples to some 2D field, which abstractly I'll write phi i, but think of as, say, a vertex operator in. And I'm always taking spacetime to be Euclidean and leaving wick rotation for some future day. So these lambda i have scaling dimensions, the first term in the beta function, which are of the form spacetime momentum squared, minus, slightly negative, where I'm using dimensionless units for spacetime distance. And these are all going to be very small in dimensionless units. I'm only interested in very long-distance physics in dimensionless units. So in the language of the renormalization group, these coupling constants are slightly irrelevant. They have slightly negative dimension. So under the flow, they're driven to zero under the renormalization group flow. That's the idea of stability. Now, let them become sources in two dimensions. So let the coupling constants vary over the surface. And then set them fluctuating, make them into two-dimensional fields with a natural action. So this is a sort of meta nonlinear model, where the target space is that curly m, the space of spacetime fields, where lambda i's are coordinates. And the action is given by the natural metric on the space of spacetime fields, roughly the L2 metric, modular gaugian variance, which is in the limit where the target manifold is big, is the natural metric on the space of 2D quantum field theories, as Sascha-Zamologikov defined. And then little g would be the coupling constant in spacetime, the string coupling constant. So here on the right, we have the coupling of the sources to the local two-dimensional fields. And then in the middle there, we have the exponential of the action of this meta nonlinear model. OK. So in this functional integral over the lambda i sources, I want to do the two-dimensional renormalization in the Wilsonian sense. I want to integrate out fluctuations of the lambda i at small two-dimensional distances, less than capital lambda inverse. So when we integrate out fluctuations, we're going to be producing insertions of the phi i in the surface smeared by some functions of z, which are over distances less than this distance lambda inverse. And this action was designed so that these insertions of the phi i would be the same as the insertions produced by tiny handles attached to the surface, what would be produced by string theory quantum corrections, but only the quantum corrections that are local in two dimensions, where the ends of the handle are close together at this two-dimensional distance scale. So this, when I say the lambda model acts, what I mean, I mean the two-dimensional renormalization group in the lambda model, it acts to produce an effective, these insertions of the phi i's, produce a new two-dimensional field theory, but with a cutoff at this scale, big lambda inverse. And this is what I claim is the quantum string background, this two-dimensional field theory cutoff at this scale, big lambda inverse. So what the lambda model is doing at smaller distance scales is calculating the effects that the froth of small handles would have produced. Now, we only understand, even in principle, how to calculate the effects of those small handles perturbatively. But this two-dimensional field theory is a sensible two-dimensional field theory. It's non-perturbative. So this is a non-perturbative construction of the quantum corrections to the world surface at short two-dimensional distances. And the crucial design principle here, that this limitation to handles that act locally on the surface, is two-dimensional locality. So that at two-dimensional distances larger than this cutoff, we have a local two-dimensional field theory. So string theory, the calculations of the string S matrix will work. They depend on integrating correlation functions that are non-singular except when vertex operators collide. So here, this effective 2D field theory will have that property at distances larger than this cutoff. OK, now, at the same time, a measure on the lambda i is being produced. So before we've allowed the lambda i's to fluctuate locally, you would have some value for, you'd be in some quantum field theory at very short distance. And it would evolve under the renormalization group along a trajectory. So points in curly m would evolve to different points in curly m. The beta function is the renormalization group is a flow in the space of quantum field theories. But now, the lambdas are fluctuating. So when you integrate out the short distance fluctuations, you might start with a point, some specific 2D quantum field theory, but you immediately get a measure on 2D quantum field theories as you evolve. And the 2D renormalization group of the lambda model drives that measure to a limiting equilibrium measure. That's the generalization of driving to a fixed point. So the picture is, well, to study what's going on, take some observable at z in this theory. That's a function on the spacetime fields, a function on the 2D coupling constants, a function on this curly m. And under change of scale, well, the coupling constants will evolve in the beta function. But there will also be noise. And you can see this as expanding lambda in the soft modes plus the fluctuations. And you'll get a two-point function of the fluctuations that produces two derivatives of f and some short distance correlation that will go as the inverse of the coupling in the action. So then if you just look at the evolution of the dual measure, it evolves as a random walk in the space of quantum field theories driven by beta, which was the picture I tried to give in the previous slide. So you're being driven to the fixed point, but there's noise. So you wind up the asymptotic equilibrium is a measure concentrated near the fixed point but with some distribution around. Now, if the beta function were 0, it would just be covariant random walk on the target manifold. So you'd be driven to the metric volume element on the space of quantum field, on the spacetime fields. If the beta function is the gradient of some function s on spacetime field, then the equilibrium measure will be the metric volume element times e to the minus s. So one gets quantum field theory in spacetime as the equilibrium measure under this flow. Another way to picture this production of a measure is in the radial quantization. So then you have loops in the target manifold are evolving under dilation, two-dimensional dilation. The non-zero modes are strongly suppressed. So the ground state wave function will be concentrated near the constant loops. So the ground state wave function under the radial quantization, its evolution will be just essentially stochastic quantization of the spacetime quantum field theory. It's just driven under the gradient of the spacetime action with noise. And then the distribution around the constant modes would be governed by the target metric. You'll have some Gaussian wave function around the constant modes plus corrections. And that contains all the two-dimensional physics. All right, now what's the role of this cutoff in the effective two-dimensional surface? So doing string theory, one always just uses coordinate z and takes absolute z minus z1 minus z2, such quantities. I want to think in terms of more physical two-dimensional terms. So I imagine that our two-dimensional quantum field theory, which has couplings lambda i, is renormalized at some two-dimensional distance, mu inverse. And our cutoff is much smaller than the scale at which the two-dimensional quantum field theory is renormalized. So this number, big lambda times mu inverse, is very large. So we have a two-dimensional theory renormalized called a macroscopic scale, distance scale mu inverse. And we're doing these fluctuations in the coupling constants at a very tiny two-dimensional scale, big lambda inverse. So when you have an irrelevant operator, an irrelevant coupling constant, the effects where we want to use them at scale mu inverse are strongly, well, are suppressed by a power of the difference of scale, where the exponent is the dimension of the coupling constant. So there's the dimension of the coupling constant, there's the ratio of scales. And I write it in this form, e to the minus l squared times the spacetime momentum squared, where l squared is the logarithm of the ratio of two-dimensional scales. So what we see is the wave modes of the spacetime fields at high momentum are cut off. So we can simply, they are really irrelevant. The ones at small momentum are almost marginal. But the ones with large momentum in spacetime are genuinely irrelevant. And we can disregard them. They have no effect. The corresponding insertions have no effect on the macroscopic two-dimensional physics that we're going to make use of, let's say, for string S matrix calculations. So this spacetime distance l gives an effective ultraviolet cutoff in spacetime, which renders the target manifold effective of the lambda model effectively finite dimensional. So it really is a sensible two-dimensional theory. So we have a correspondence between the two-dimensional distance scale at which divides where the lambda model fluctuations take place from the effective world surface that corresponds to a spacetime distance scale l. OK, so usually, as I said in the beginning, we just take mu equals 1. And then this lambda inverse would be a dimensionless number, which would cut off the integral over moduli in string theory calculations. But I prefer this more physical feeling interpretation. Now, when we're doing string theory calculations and have a two-dimensional in the effective world surface, this becomes the ultraviolet two-dimensional cutoff. And when we integrate over the moduli, say, for a tube in the world surface, we wind up with a propagator that is not 1 over p squared for each mode, but has a contribution, a cutoff, an ultraviolet cutoff, in two dimensions. So you notice that for large p squared, the number in parenthesis is very large. So for large p squared, we just get the 1 over p squared. But for small p squared, the pole is eliminated. So in the string theory in this effective world surface, we have a cutoff in the spacetime infrared. So this effective string S matrix is only described scattering at spacetime distances up to big L. And the quantum field theory, the lambda model has only lambda i's wave modes of the spacetime fields at distances larger than L. So the quantum field theory that produced describes physics at distances larger than L, and the string scattering the S matrix is at distances smaller than L in spacetime. And that choice of big lambda was arbitrary. So we can vary L at will as long as it's large in dimensionless units. And this construction, I suggest, the effective world surface and the spacetime quantum field theory are constructed by this two-dimensional model guarantees that these will be consistent. So if you choose L large and describe some physics by a string S matrix or choose it smaller and describe the same physics by quantum field theory, they should agree. So I think of this as a realistic version of the string background, where you have a quantum mechanical description of the apparatus in which scattering experiments take place. That's what we ought to have if we're going to do a physical string theory. And on a philosophical level, it seems like a practical theory. The religious S matrix theory where everything is an S matrix, that's, I think, an idealization that doesn't have anything to do with how we really have done physics. We describe all that we see by quantum mechanics. In particular, we describe CERN by quantum mechanics. On the other hand, the notion that we have quantum field theory all the way down indefinitely in this sense, that seems also an unnecessary idealization. OK, finally, in this presentation of the proposal, I point out an intriguing property. The two-dimensional physics, this two-dimensional renormalization group in the lambda model, that's operating from small two-dimensional distances to larger. That's how Wilson taught us to think of renormalization. I guess it goes back to the beginnings of renormalization, that picture. But given this correspondence between two-dimensional distance and spacetime distance, the quantum field theory in spacetime is being built from the largest distances downward, which is very unlike our picture of effective spacetime quantum field theory. I find that intriguing, and also might end up having some explanatory power. OK, so at this point, given a proposal, the proposal offers an endless number of formal internal questions. Describe string scattering, something's like some analog of the reduction formula. Describe string scattering in a state of the quantum field theory. That's just one of them. But I want to know if this is right or not. So I would like it to say something that can be checked against experiment. And one could fantasize that this machine, you crank it and pay careful attention to what it does, and you will end up with the standard model. But given the history of that fantasy over the last couple decades, I think it's not going to happen in my lifetime. And I really want to find this out in my lifetime. And I don't see much possibility of verifying string theory experimentally. So I took another tack. I said, OK, let's suppose that it does produce. The only way it could be right is if it does somehow under some circumstances produce the standard model. So let's say it does produce something roughly like the standard model, something that could include the standard model. Could it be that it produces something else, something exotic that you would not expect from the canonical quantization of the standard model? OK, now this lambda model is a two-dimensional field theory. It isn't stochastic quantization of the classical field theory action. It's a two-dimensional field theory. So could there be non-perturbative 2D effects that would show up in this measure it produces on spacetime fields? OK, so remind you that, OK. So now, given this assumption that we've produced a spacetime field theory that includes the standard model, curly n is the manifold of whatever those spacetime fields are, the gauge fields of the standard model, spacetime metric, the fermion fields, some scalars, whatever, on the spacetime where we're going to do experiments, which is R4. Yeah, no, no, I just mean the all connections in an SU2 bundle on R4, right? That's what? Metrics, too, sure. I mean, you know, a quantum field theory cut off quantum field theory of the metric is going to look like classical field theory to us. So that's not a particularly interesting. You can leave the metric out if you want. Yeah, but it's like a three-dimensional field. No, no, I mean four-dimensional field, OK. And everything, I'm assuming, is happening at weak coupling. So non-perturbative effects would be semi-classical effects. And in two-dimensional field theory, semi-classical effects, the ones that I know about, are given by winding modes, which come from non-trivial loops in the target manifold. And two-dimensional instantons, which come from pi2 of the manifold. So I guess this is the first, there'll be more mentions of instanton, but two of the inventors of that, two of the discoverers of that, Sasha and Sasha Polikovin-Balabin are here. OK, so the mathematicians have long known that there are non-trivial homotopy groups in the space of gauge fields on R4. And when I say the space of gauge field, I mean, of course, the physical space of gauge field, mod gauge transformations. So pi1 for SU2 gauge fields, there's one non-trivial loop in the space of gauge fields. That first came into physics, I believe, with Witten's discussion of global anomalies in SU2 gauge theory. And pi1 of the space of SU3 gauge, all the other pi1s vanish. So there's one winding mode that might be interesting, and that's for SU2 gauge fields, which, of course, we should have. Pi2s are always non-zero. There's one non-trivial two-sphere for SU2 gauge fields, and there's a whole integer worth of such two spheres for SU3. So winding modes in a two-dimensional field theory give new local fields. So those, you would think, would correspond to new degrees of freedom in the spacetime theory. So the question is, are these low-energy degrees of freedom? Of course, they would be not canonical because they have nothing to do with the spacetime classical action. And then these two spheres would give 2D instantons, and one might expect they would give non-canonical couplings in the 2D field. But I find the first question more interesting. So I haven't done much with the second. OK, but I wanted to know what those loops look like, because if you're doing a quantum non-linear model with these spaces as target manifolds, the winding mode would be given by the minimal loop, the shortest loop you can find. And if that loop has finite length, it's going to be a high energy, a very massive excitation, and we can forget about it. So the only possibility is if that minimal, if there's a loop of zero length that's topologically non-trivial. So I investigated this in a very roundabout way. And it turns out, after I reported my results to the mathematicians that they basically knew about it, but I had to find it out for myself. And I didn't really look, well, it's a somewhat long story. But what I found was that the non-trivial loop in the space of SU2 gauge fields is a loop of gauge fields which consist of an instanton and an anti-instanton. Now, these are four-dimensional instantons, the original instanton. And then pi 2 for SU2 gauge fields, you need two instantons and two anti-instantons glued together. And then you modify the gluing parameters and you find a non-trivial two-sphere. And for pi 2 of SU3, it's, again, an instanton, anti-instanton pair. But the interesting thing is that the minimal loop has zero length, and the minimal two-sphere has zero area. So there's a chance of low energy physics here. And as I said, I find the possibility of non-canonical degrees of freedom, given the mysteries we have in physics, that's tantalizing. So that's the one I've been thinking about. OK. So I mean, how much time do I have? Or am I up? Oh, fine. So here's the construction of this non-trivial loop. You take an instanton on R4, and then you glue in a very small anti-instanton. So A plus is the instanton, and it has size rho plus, and it has a center, x plus. So x plus is in R4. And there's a possibility of an internal rotation in SU2, but you fix that by global gauge transmission. And then you take an anti-instanton, a very small size rho minus centered at another point, x minus, and you rotate that by an element of SU2 acting in the adjoint. And then you glue it in to the instanton. Well, the possible ways you can rotate that anti-instanton are given by SU2 acting in the adjoint. So the parameter space is SU2 mod the center, plus or minus 1, so SO3. And that has a non-trivial loop in it. Pi 1 of SO3 is Z2. And that loop in this family of gauge fields is a representative of the non-trivial loop in the space of gauge fields. One can show that very explicitly. How do you know that it can be contracted by modifying these solutions in some other way? Yeah. No, you can explicitly show that you go around the loop and you get a gauge transformation that is explicitly the gauge transformation that cannot be contracted to the identity. Well, that's about statement about the space of SU2 gauge field. Why does it come from instanton?  Yeah. So I'm constructing a loop in that subspace and then verifying that that loop is non-trivial in the space of all gauge fields. And you mean that it's a sub-dual gauge field? Where does it come from? It's a combination of those. Oh, that comes only if you take a plus and a minus to be one piece and to another, I think that's essential. The gluing, yeah. You have to glue. This has topological number 0. This is in the, all right. So I want to, but we are doing, we need to have the metric. We want to find out what's the length of this non-trivial loop. So again, this is from the mathematicians. OK, so we parametrize that anti-instanton that we're gluing in. Well, leave the location fixed. We parametrize the size and the internal rotation in SU2 by an element in C2. So we take a reference point in C2. We apply the SU2 rotation to it, and we get an element in C2. So that's the standard parametrization of SU2 by C2. And then we multiply, but it's also the two-sphere. I'm sorry, the three-sphere in C2. And then we take the radius to be rho minus. So we get an element in V minus in C2, which parametrizes the size and the SU2 rotation. And then we calculate the metric. Take small perturbations. Take the L2, mud out by gate transformations. Take the L2 inner product. And the metric is smooth in this parametrization at the origin. And the actual metric on the instant time modular space has nice properties. But here, we only are talking about near the origin, where the instant time, the anti-instant time decouples from the instant time. When rho minus is finite, you have to glue them together. You're not in the space of self-dual. You don't have the nice mathematical properties. But anyway, the metric, remember, has a 1 over coupling constant squared. And then it's just the Euclidean metric in this space C2. And the non-trivial loop, that's the loop in G minus. So it's a loop in the three sphere. Oh, V minus is only defined up to plus or minus 1, because G minus is only defined up to plus or minus 1. So we're really looking at the orbital C2 mod Z2. So we're looking at the non-trivial loop from the north pole of S3 to the south pole of S3 for any given size, rho minus. If we take rho minus to 0, the length of that arc, that longitudinal line, goes to 0. So the minimal non-trivial loop has 0 length. So in the lambda model, the winding mode for such a loop is just the twist field for this orbital. And we did this for fixed values of the location of the instanton and the anti-instanton, and for fixed size parameter for the instanton. So they're collective coordinates. And now, again, given this assumption that we somehow got a field theory that includes the standard model, we'll have fermion fields. And those coupled to the SU2 gauge field, and they'll have zero modes localized in the instanton and in the anti-instanton. And it's very pretty. You can actually show how, as you move in this non-trivial loop, the zero mode in the anti-instanton changes sign. And that's an explicit realization of this SU2 global anomaly. But when we do an orbit folding, we project out all the two-dimensional degrees of freedom that are odd under the Z2. So we project out the zero modes in the anti-instanton, this tiny anti-instanton. And we leave the zero modes in the instanton. They survive. So it looks like there are possibilities for interesting quantum numbers in this object. But at this point, I want to emphasize that it's a bizarre looking object. It's bilocal. It depends on two points in spacetime, x plus and x minus. And then this additional parameter, rho plus. There's an analogous object, the Cp transform, in which you have an anti-instanton with a tiny instanton embedded. Anyway, it looks very bizarre. But this orbit folding, where you eliminate the degrees of freedom that are odd under the Z2, it looks like that ought to make sense of field theories which have global SU2 anomalies. Because this gets rid of the global SU2 anomaly, but leave that. OK, we need to understand the flow in this neighborhood. And one can actually calculate the Yang-Mills action, of which the flow is the gradient. I'm not going to go through the details. But you find that there is one unstable direction. So there's a trajectory. So you have a fixed point. I normalize the Yang-Mills action, so the instanton has action 1. So we have an instanton and an instanton. That gives 2, plus something proportional to the sizes, at least one of which is small. And most of the form of that is determined by conformal invariance in R4. But if you study the behavior near, so you have near the fixed point when the little anti-instanton has zero size, that's a fixed point. That's a genuinely self-dual field. You study the behavior near that. You find one unstable direction. So there's a flow that leaves from near this fixed point, this non-trivial fixed point, and flows down to the flat connection. And then interesting things happen when both instantons become small, but the flow becomes sort of like asymptotically free. You don't have actual instability, but just marginal instability. So at this point, my thinking is still quite muddled. The question is how these degrees of freedom will contribute to the spacetime physics, if they do. So my best understanding of how to proceed is to introduce new coupling constants that couple to this winding mode and then study the dynamics. I mean, one can fantasize all sorts of things, a condensation, well, who knows. But in order to study the dynamics of these couplings, one has to know the beta function of these new degrees of freedom. So one has to understand how products of the twist field and ordinary two-dimensional fields evolve under two-dimensional scaling. And in particular, zero length just guarantees that the energy will be zero classically. But we know from ordinary orbitals that the twist field, the scaling dimension of the twist field gets quantum corrections immediately at one loop. And the question is, they would ruin this idea of low energy excitation. So that has to be checked. And then it seems to me the basic object that is this unstable trajectory from the instanton-anti-instanton pair down to the flat connection. But I have yet to work that out. Thank you. Any questions, please? So it looks like the lambda model is actually it's a single model on the product of the original spacetime manifold and the spacetime model. No, no, no. I mean, you can think of it that way. I think it's, yeah, but it seems to me to analyze the structure. It's important to understand that the couplings lambda i, which in this picture are the fields on spacetime, they have non-trivial renormalists. They aren't dimensionless. They have dimensions that come from quantum corrections in the original nonlinear model. And the structure of the lambda model is based on the quantum properties of the original two dimensional field theory. So I don't think it's all that useful to study them, to quantize them simultaneously. The picture I presented is, first you quantize the original model, and then you add fluctuations of its quantum coupling constants. I mean, it might be that there's some fruitful way to do it all at once, but it hasn't seemed like that. Another option would be to do some spin glass model, when you first quantize the way you say it. The original model, then you take a, you know. That's interesting. Yeah, I have no idea how to, but that's very interesting. So you'd get an effective theory just, yeah, that might be. That might be. Other questions? Yes, maybe it's related to the previous question, but somehow M is the space of all 2D quantum field theories, and you use it to build another quantum field theory, so somehow this new field, the lambda model, should be a point of M, isn't it? No. It's not all 2D quantum field theories. It's a special class. Oh, I forgot one thing I really wanted to say. Back when I started talking about string theory, that this is where Demeric Kniznick and I intersected. We were both interested back in the mid-80s in finishing the covariant quantization of the fermionic string using Sashopolyakov's supermorphism 2D ghost fields. Yes, I definitely wanted to mention that. My motivation was this, I need a covariant two-dimensional field theory. But so it's a special class of 2D quantum field theories, the original 2D field theory. And the lambda model is not a globally defined 2D field theory. It's only operating at short two-dimensional distances. So I don't think that the picture is, as you say. You refer to this twisted loops of instantons as a minimal representative of I1 over 2B. Does that mean that you have other configurations? Well, I mean, OK. So you have this parameter space, which is the size of the tiny anti-instanton, and then a three-spher of orientations, an SU2, mod Z2. But think of it as a three-spher. And the non-trivial loop goes from the north to the south pole of that three-spher. So take the size to be non-zero. Really, what you can think of this is describing, you have all the other modes of the gauge field, all the other ways, the irrelevant directions, you can go away from this family. And what this is describing is a cycle so that any loop that surrounds this cycle will be non-trivial. But for the two-dimensional physics, I'm interested in the one that shrinks down to zero. I think that we should finish now. OK. Why do you need the lambda model to study those exotics? I don't know. I think of it the other way around. I need those exotic twist fields to study because they're in the lambda model. I mean, you could go and study them, but I wouldn't have a motivation.