Martin Sasieta: "Emergence of Closed Universes in SYK"

Añadido: 2026-05-10

[00:00:18]Okay, let's start.

[00:00:25]Okay, thank you so much Samir and thanks to the rest of the organizers as well for organizing this uh really nice workshop. It's a pleasure to be back to Florence.

[00:00:35]So today I would like to tell you about some uh recent work and some upcoming work as well with uh my great collaborators Brian Swingle who's a professor at Brandeise and uh with Alejandro Var Lopez who is a postoc at UBC.

[00:00:52]Okay. So let me start trying to very broadly motivate uh the problem uh for many of you who probably haven't thought about this recently. So is there something wrong or um okay so we the the big picture is that we would like to understand how quantum gravity works uh just beyond ads space and uh well there's many reasons why we are interested in that uh is there something wrong uh Uh, no it doesn't. Let me see if I stop sharing.

[00:01:40]Okay, let's see.

[00:01:46]Seems to work. Okay. Um, yeah. So, as I was saying, the the big sort of question we are Oh, it did it again. So, Okay.

[00:01:59]Um, so yeah, I guess uh I'll continue.

[00:02:02]Uh, so the big picture question is uh that we're interested in is uh how quantum gravity works in other spaceimes.

[00:02:11]And there's many reasons why we are interested in this question. One of which is that we want to eventually apply our knowledge of quantum gravity to our own universe. Okay.

[00:02:21]And uh in particular closed spaces are interesting because uh holography as we understand it seems to run up against a very clear limitation at least globally in these spaces and this limitation is that the global holographic hilbert space uh seems to be trivial. So what this simply means in a very naive sense it just means that uh for a closed space the boundary is empty. So uh we very naively would assign an a zero entropy to an empty uh boundary and so that means that the global holographic uh hilbert space is trivial.

[00:03:01]Um okay so the puzzle is that still there could be a possibly huge uh perturbative effective field theory Hilbert space in this closed universe and uh in particular uh there could be structure like planets galaxies and so on in this effective fully Hilbert space. So the big question is what is the framework not even as an example of a hologram as we understand 50 but more of a what is the framework to actually microscopically complete gravity in this closed universe.

[00:03:38]So even though this situation might seem sort of a very exotic from ADCs pers from an ADSC perspective uh I will try to argue today that uh it is actually connected to a very common situation in ADSCF and uh this situation is uh the black hole interior. Okay, so in ADSCFT we know that uh the CFT describes black holes at high temperatures and we know that these black holes have interiors and so there can be situations in which the interior of a black hole accommodates a very large uh uh perturbative uh effective theory entropy.

[00:04:17]So uh here what I'm showing is a picture of a spacetime uh for a bag of gold spacetime. Yes.

[00:04:27]Yeah. Yeah. Sure. Sure.

[00:04:31]I tried to stop sharing and shared it again though.

[00:04:45]Sorry.

[00:04:47]Uh I guess I do have uh the other one.

[00:04:50]Let me see.

[00:05:09]Okay. Zoom. Where's Zoom? Here.

[00:05:14]Uh share this one. And then uh no view uh full screen mode.

[00:05:27]And uh what do again?

[00:05:51]Okay.

[00:05:54]Stay.

[00:05:58]Okay, it's metastable at least. So, okay, I guess that's good enough. Okay, so uh yeah, as I was saying, the situation in ADS50 where a similar story happens is the black hole interior. Uh so this is a bag of gold spacetime and this corresponds to a time symmetric slice of this bag of gold. uh there's the horizon which is some minimal surface and uh the CTF describes pretty well what happens outside uh but in principle there could be arbitrary large entropy inside and so uh that seems problematic from the point of view of uh just conventional ads because the uh that means that the effective field theory entropy can uh exceed by a large amount the holographic entropy uh uh given by the beckenstein hawking entropy. Okay, so just in a very nice way that also means that all the quantum information over here cannot be encoded in the CTF Hilbert space at least not in a conventional way.

[00:07:02]Okay.

[00:07:03]So today I will try to uh tell you something about closed universes from this perspective and I will mostly focus on closeness. I won't be so interested in phenomenologically interesting uh universes like those that inflate or the sitter space and uh in particular the reason is that I will try to relate the physics of closed universes to the physics of the black hole interior which is itself some cosmological spaceime okay so what is the uh main observation in ads to try to describe closed universes well the main observation is that uh there are wormhole solutions space-time wormhole solutions uh contributing to the gravitational path integral which prepare semiclassical states of a closed universe. Okay.

[00:07:57]So here I mean these these solutions are not very exotic and uh to illustrate this I will just write down some solution in three dimensions which look like this. So this is a solution in pure dimensional uh pure uh gravity in three dimensions and uh uh the solution looks the metric looks like this. TOAO just parameterizes the longitudinal direction on the wormhole. TOAO equals plus minus infinity corresponds to the location of space-time asintotic boundaries.

[00:08:26]And here this kosh uh factor is the scale factor in an FRW type of uh solution. And this sigma just parameterizes the metric of the transverse uh slices to this uh solution. So for this to be a solution to pure gravity then uh sigma has to be a hyperbolic reman surface. Okay for that you need uh genus two or higher.

[00:08:54]So if we add massive point particles to the theory we can construct spherical uh wormholes with the spherical boundaries and they have the same metric. Now uh given that the uh spheres contain three punctures the sphere ads a hyperbolic metric and this again becomes a solution uh to uh the three-dimensional Einstein equations. Yes.

[00:09:21]>> Yes.

[00:09:23]>> Okay. I will I will this will be my next slide. So what I mean is that uh if you cut this wormhole in the middle uh this prepares some state okay in the closed universe and uh this state is semiclassical if you want to think of uh uh uh you know state as a function of the metric and the extrinsic curvature.

[00:09:45]This is semiclassical in the sense that it looks like a coherent state. It's centered around some given uh uh solution. Uh but it is some state uh over there.

[00:10:02]>> Yeah.

[00:10:04]>> Yeah.

[00:10:12]>> Yeah.

[00:10:13]>> Yeah. Yeah. Yeah, in principle this the the wave function of the closed universe defined in a very abstract way could also have uh other topologies contributing could have other spatial topologies as well but I guess this is like the most uh conservative uh interpretation of this uh ukidian saddle as preparing some state which is sort of semiclassical um and uh what this means as I was telling is that If you take this uklidian wormhole and analytically continue to real time, the metrics the metric looks like a big bump big crunch closed universe where the spatial slices are given by sigma. And so uh in Lorenzian time this wormhole prepares a state which initially starts at some given with some given volume and it crunches towards the future and towards the past. Okay.

[00:11:08]Now question no. Okay. Uh so this kind of interpretation is interesting uh like this kind of a uh uh the emergence of of closed universes from wormholes is interesting because it allows us to interpret how the closed universe or how the wormhole emerges from the CTF. And so currently what we believe is that the wormhole or the closed universe wave function in this case it emerges from a statistical average over CFT partition functions and uh in particular for the worm for for a wormhole to prepare a state the two CFT partition functions have to be equal. Uh one can also consider situations in which the moduli of the two boundaries are different and this would be interpreted as some sort of uh overlap between two different uh closed universe states and in particular Gabriel gave a nice talk last week about uh positivity constraints of these overlaps. Okay.

[00:12:10]So yeah the the issue I guess in higher dimensions is to try to define this overline uh uh precisely uh uh and this is a non-trivial task but uh I would say that in in 2D 3D gravity uh this is sort of uh very well understood uh by now okay and the idea is that these numbers that come from the CTF partition functions they are very erratic numbers because they contain heavy stuff which comes from the heavy sector of the CFD. And so uh these numbers are erratic because there's quantum chaos happening at at high energies in the CFD. And so uh the what the gravitational path integral is doing is that it is uh averaging over these uh all of the phases which are very erratic and is giving us some smooth uh quantity. Yeah.

[00:13:02]>> Yeah.

[00:13:05]>> Yeah. Yeah.

[00:13:08]I think we understand.

[00:13:12]>> Yeah.

[00:13:14]>> Yeah.

[00:13:18]>> Yeah.

[00:13:31]>> Yeah. will not have as much.

[00:13:41]>> Yeah. Yeah. We we are you talking about offshell contributions or they can be like on shell.

[00:13:47]>> Okay. Yeah. I'm I'm I guess I'm talking about situations where uh this thing is dominant. Uh I mean you you can call it the norm of a state or you can call it C grab if you want but it can be Yeah.

[00:14:09]>> Yeah.

[00:14:12]>> Not even that one side is included in the other neither side.

[00:14:17]>> Um Okay. Yeah. I don't know. Maybe we can talk later. Uh but yeah. Um >> yeah.

[00:14:29]classical because you can have many complicated hyperbolic.

[00:14:34]>> Yeah. Yeah. Yeah. and and then some of them that contribute for example to the right hand side not even have nice >> okay but in this in these situations the like the ones that I'm going to talk in my talk this is the dominant uh solution probably no uh connected dominant solution always um yeah That's one of the gravity.

[00:15:13]>> Yeah.

[00:15:16]>> Yeah.

[00:15:16]>> There's many different ways.

[00:15:21]>> Yeah.

[00:15:29]>> I I guess I'm not preparing the hard hawk instead of the genus 2 uh service.

[00:15:33]I'm just preparing this state which is specified by the boundary condition. So it's not a hard hawking state. Uh well I I give you the wormhole and this is the state. Uh yeah but this is that's my choice of state and what I'm telling you is that I know how to interpret the wormhole in the boundary. That's all I'm saying.

[00:15:54]Okay.

[00:15:56]Good. So yeah in some cases this uh average can be interpreted as as some uh explicit interaction between between the two boundaries. Um well that is always true that an average can be interpreted as some explicit interaction. The interaction is typically very hard to write down but uh sometimes this interaction is local and this has been studied in these papers. Okay my talk is not going to be about this about this interpretation. it's going to be about explicit uh constructions and then uh we can discuss interpretations.

[00:16:32]So yeah the idea is that yeah this kind of uh emergence of spaceime seems very different to how we believe uh ads works. So in ads we're given some bulk state and we have uh some boundary state dual to it and we know that the CTF microscopically completes this bulk stage. Okay.

[00:16:53]uh here on the other hand we have some closed universe state and in the boundary side the best we have is some a bunch of numbers and some statistics of these numbers. So this seems uh kind of confusing and uh however the the two pictures are connected. They are sort of continuously connected and uh the the point is that uh well in this paper already three years ago what we did was to take these two boundary partition functions and then we just connected them uh together through some tube. uh actually this is not what we did in our paper but I'm borrowing uh you know analogous ideas in three dimensions developed in this in this paper. So uh yeah uristically this is what we did we we in reality what we did is we started with a higher dimensional construction uh but but this is sort of the the conceptual uh story.

[00:17:55]Okay. So once you include this uh tube over here of length beta then the quantity becomes a single boundary uh CTF quantity. So in particular in this case this thing is a sphere uh sixpoint function uh in some in some uh frame.

[00:18:10]Okay.

[00:18:12]And so once you have this you have a conventional uh CTF interpretation.

[00:18:18]Essentially you cut this uh tube in half and what this does is that it prepares some CTF state on the boundaries of the of the tubes on the sphere on the on the circle.

[00:18:31]So this should be conventional CFT where we now should be uh able to uh use the conventional holographic dictionary to find the bulk saddles contributing to this boundary problem. And so the statement will be that any bulk saddle which dominates uh this problem uh the bulk state that this saddle prepares which is s x of beta this should be the bulk dual to the boundary state five of beta and in this particular example I'm going to be working in in pure 3D gravity with a bunch of point particles.

[00:19:11]So the the point is that there's two uh saddles which contribute and there's an exchange in dominance uh between the two as a function of beta as a function of the uh length of this tube and uh this exchange in dominance is essentially very similar to the hawking page phase transition in ads.

[00:19:32]Um so the first saddle dominates at low temperatures when beta is very large. So when beta is very large essentially the only state that propagates over here is the ground state and may maybe like a few excited states which are low lowlying and so this kind of saddle is very similar to the two boundary uh sphere three point wormhole that I was talking about before at high temperatures what happens is that the three conical defects propagate through the interior of this uh of this cylinder and uh this the bark s looks completely different. It's not a sort of non-handle body, but it's some handle body of the of the sphere.

[00:20:14]And uh when you evaluate the gravitational actions uh essentially if you take the masses of the operators to be very large, their contribution factorizes and is the same in both saddles. But this kind of saddle uh you can think of uh the warlines of the m of the masses as pinching off. So this effectively reduces the gravitational action of this saddle effectively reduces to a thermal ads partition function at inverse temperature beta.

[00:20:44]And uh for this one this is hard harder to imagine but what happens is something similar and uh what you end up getting is something which looks like the uh uh BTC uh partition function at inverse temperature beta. the high temperature uh phase dominated by uh card entropy and this is dominated by cmir energy at low temperatures. Okay. So when beta is of the order of the hoging page uh inverse temperature there is some exchange in dominance between the two saddles.

[00:21:18]So what does this mean for the bul dual to the to the state the CTF state that we were preparing. So what this means is that at high temperatures the dominant solution is was this one and if we take an analytically continue across the time symmetric bulk slice what this is is a state of a black hole where the threepoint particles are in the interior of the black hole and fall into the singularity. So this represents at high temperatures a black hole a pure black hole microate uh where the threepoint particles are in the black hole interior.

[00:21:51]low temperatures. What happens is that uh the dominant solution is this one and this thing prepares a state on a spatially disconnected closed universe with the three-point particles and then additionally some ads space uh which is completely disconnected from this closed universe because this is a finite temperature situation uh the bulk fields in the ads will be entangled with the closed universe. So even if the closed universe will be especially disconnected from the ads region there will be some order one entanglement between the quantum fields. Okay.

[00:22:28]So the picture is that uh we start with a black hole with a bunch of stuff inside and we cool it down below the hawking page transition. The black hole interior decouples especially become some closed universe.

[00:22:44]Okay. Yeah. This was my higher dimensional part of the talk. Any questions about this?

[00:22:52]Yes.

[00:22:58]Yes. So they have to scale with C essentially. They can be below the black hole threshold. They can be conical defects below the black hole threshold.

[00:23:08]The sum of the three masses has to be larger than some uh threshold for this to be a solution. But uh individually each of them have to scale with C. Yeah.

[00:23:20]Well, because the the the point is that they have to back. So for the sphere uh essentially you need the sum of the opening angle for this to admit a hyperbolic metric. The sum of the opening angles has to be something and the opening angle is related to the conformal dimension of the defects.

[00:23:43]Well, in that case, you won't be able to have this kind of solution because you need the the matter to back react in order to stabilize the wormhole. So, you need always heavy matter. Um, but uh in principle you could think of turning on very large uh boundary values for some scalar field and that could uh lead to this kind of solution. For example, people talk about this axon wormholes. Um, in that case, this is just some scalar which stabilizes the wormhole.

[00:24:17]Okay.

[00:24:20]So, yeah, there's many confusing things about these uh these uh setups uh as Alex was pointing out some of them, but there's many more. And so what we wanted to do is to find a similar situation in a much simpler model with the goal of trying to understand the this emergence of this closed universe microscopically.

[00:24:44]So the model that I will talk about today is the uh syk model. It is a model of nayana firmians which interact uh but given by this Hamiltonian and uh the couplings in this model they are gausian random correlated random variables.

[00:25:02]So this model is holographic because at low temperatures it is it is described by a mode which universally describes near extreal black holes. It is this swarchen mode. However, this model is not useful for our purposes uh because uh the model doesn't contain a a thermal phase transition at finite temperature.

[00:25:21]So essentially the low temperature phase is uh nearly conformal and there's no such a thing as a hawking page phase transition. It's a first order phase transition.

[00:25:33]So what we did is to instead consider this other uh model which corresponds to two SYK systems coupled by this particular uh bilinear ultra local coupling. So the reason to consider this model is that uh it is famously known that this model contains a thermal first order phase transition at large end and uh moreover this model is holographic at low temperatures low enough temperatures compared to the SYK couplings it is described by an ADS2 solution.

[00:26:07]So the state the physics there is that the low temperature phase of this model corresponds to some uh empty ads to wormhole which is traversible. So this is essentially the same picture as having an empty higher dimensional ads.

[00:26:24]Okay. So uh in this case it's not just some uh well ads 2 has two boundaries.

[00:26:29]So this is why we need to sk uh systems with this coupling. But essentially the point is that global ads 2 is the solution which describes the ground state of this uh of this system and uh for us global ads 2 will play the analog of emptys in higher dimensions.

[00:26:50]Essentially global ads 2 is gapped. If you put some matter on global ads too it will have gapped exitations uh high temperatures. However this model uh describes a pair of black holes. So it's similar to uh the higher dimensional uh setup where high temperatures the CTF describes a black hole.

[00:27:12]Good. So let me explain this a little bit better. Yes.

[00:27:22]Uh global ads 2 is zero entropy. It doesn't have a classical entropy. Well, it has the quantum fields there. I guess finite temperature or zero temperature.

[00:27:35]Yeah.

[00:27:39]>> Yeah.

[00:27:42]What's the coupling?

[00:27:47]>> Oh, they are the same couplings. Yeah.

[00:27:49]They have some uh some fmians like this.

[00:27:52]And you took you take the two uh models to be identical copies. Um Uh so are you worried about the fact that these models have a zero temperature large and entropy? Yeah. The point is that the ground state of this Hamiltonian is very different from the ground state of those. Yes. So essentially the point is that the ground state of this Hamiltonian is a single state in the double hbert space and this state looks like a thermopil double. So it's some unique state and that's the reason why it has zero entropy.

[00:28:31]Okay. So yeah, the low temperature phase is global ADS2. It looks like this. Uh high temperature phase, the interaction is completely irrelevant and you end up with two black holes. And here you can think of the boundary particles as describing each SYK system.

[00:28:52]And uh the wormhole phase becomes traversible because the interaction is very important here. And the interaction introduces negative energy. Okay.

[00:29:02]Um, how am I doing with time?

[00:29:05]Yes.

[00:29:18]Uh yeah well I guess that depends on many things. It doesn't only like it depends on the strength of your interaction and things like that. Um so yeah the the the the high temperature solution is literally well you can neglect the coupling effectively. Uh uh maybe you can the point is that it doesn't affect the large end uh saddle point. Maybe you can for like there's a bunch of quantum fields over here like fermians in SYK over here and because these are actually coupled there's some way to transfer information but because you're looking at high temperature it doesn't affect the classical uh swarch trajectory so you still have a black hole I guess you can think of this as like what you want to do is a teleportation protocol but for the bug fields Okay.

[00:30:17]Yes.

[00:30:18]Yes.

[00:30:24]Yes. Well, no, you you can solve this thing exactly for the for the coupling if you want, but what I'm saying is that the coupling is negligible.

[00:30:38]Yeah.

[00:30:41]Yes.

[00:30:43]Uh essentially the point is that well there's a long story on this uh but the the point is that each of each black hole has its own swartum and uh the only gauge invariant variable is some length that connects them together.

[00:31:01]Uh yeah yeah you can have more than like copies of this thing for example. Uh yeah well I'm describing like very well you can find all of this stuff in Matina paper is not uh what what uh I'm going to talk about but anyways um okay so yeah as I was telling you the actual description of this thing is in terms of some renormalized geodessic length which connects the two boundaries and the classical uh effective action is some non-relativistic particle subject to some potential which is this exponential potential famous from JT and then the coupling what it does is that it modifies this potential for this to hold the coupling has to be sufficiently small so if you actually like introduce a very large coupling you act you're quenching the system and you lose track of all of this kind of description but anyways um high temperatures means that uh uh the particle the length the normalized geodistic length starts at energies which are positive in this potential and so it just bounces across this potential and this is why uh the solution is the two black hole solution and essentially the difference between the effect the effective potential with and without the coupling is of order mu uh times beta. So that's kind of negligible at high temperatures. Uh however the point is that the coupling introduces this negative energy and it uh deforms the potential so that it now contains bound states and so the low temperature phase is just some bound state of the renormalized geodistic length and this is why it just bounces.

[00:32:53]So you get a global ads solution.

[00:32:58]Okay. So what we did is to use this model to uh construct situation which is similar to the high dimensional situation that I was telling you about.

[00:33:09]Uh so essentially we start with some operator O in SYK and we take the conformal dimension of this operator to be very large. So we can think of this operator as a very heavy uh mayorana string and uh what we do now is we just cool this uh state down. So we we write down this operator as a two-sided state and we cool it down at some finite temperature. So this is known uh in the literature as a thermal pure state.

[00:33:37]Okay. So we have this specific uh micro state of the two coupled SYK systems.

[00:33:46]And the point is to find the bulk dual to this microate as a function of the inverse temperature beta. And uh to do that we consider the norm of this state.

[00:33:57]So we introduce two operators, one in the brown, one in the K. There's some e to the minus beta h evolution in between the two. Uh this h is not a single-sided Hamiltonian. It's just a two-sided Hamiltonian which couples the two contours together.

[00:34:16]So at high temperatures, the dominant solution is the disk. uh the particle just propagates from uh bra to k and uh uh it modifies the effective potential for the reormalized jodic length but there is a very standard solution and again because the temperature is very large you can neglect the coupling and so these solutions they have been constructed in JT uh their uh solutions they're very similar to this the so-called partially entangled thermal states constructed in this So the high temperature phaso dual to this micro state of 2s yk system describes a two-sided black hole near extrema black hole uh with a matter particle in the black hole interior and the length of the wormhole is stretched because of the back reaction of this matter particle.

[00:35:08]So again how is this described? Well, we go back to our favorite uh effective action which is this length theory and uh what the heavy matter operator does is that it inserts some conformal primary of the SL2R uh isometries of the of ADS2 and uh this modifies the effective potential with this term. So essentially it lifts the effective potential.

[00:35:33]Uh so uh what happens now is that the length variable just bounces again even if the two sides are coupled together because there's this matter particle uh the two uh uh boundary particles just bounce as they do in this uh uh black hole solution.

[00:35:55]Now low temperatures the dominant solution uh to the gravitational path integral comes from a higher topology comes from a disk with a handle. So uh the point is that the heavy matter particle just propagates through the handle and uh the uh the this stabilizes some modulus of this handle. So this is a class semiclassical solution. the the bottleneck of the handle is stabilized by the heavy matter particle and the other modulus of this handle which is the the length between the distance between the two mouths of this wormhole is stabilized by the fact that there's some interaction propagating through here. So the the male interaction stabilizes uh this solution and you need both of them for this to be a a semic-class solution.

[00:36:51]So this kind of solution at the level of the on shell action is topologically suppressed by e to the minus 2s not however it's energetically favored for the reason that it looks m so it looks like the maldeny ground state and so since we're comparing free energies and the mathnachi ground state is at that energy which is much below the the black hole phase the gap between the ground state and the black hole phase scales with n there's this competition happening and this is why this non-trivial topology can dominate and the gravitational path integral yes so essentially the if you analytically continue uh this saddle to see what state it preparers it prepares some global ads2 which is the maldenachi ground state and then there's this closed universe uh which is entangled to Yes. So the mass of the heavy operator doesn't contribute to the energy the SYK energy for example. Yeah. That also happens in the black hole interior by the way. In the black hole interior the because the operator was behind the horizon it's rest mass didn't contribute to the ADM energy.

[00:38:12]And uh well this is a very nice uh I think uh thermal phase transition between uh again black hole integer and a closed universe. But one could ask about some dynamical version of this where we start with some black hole with a bunch of stuff inside and we maybe let it evaporate. And uh in an upcoming paper alian friends they're going to actually describe a very similar story.

[00:38:38]Okay, so let me give a little bit more detail about what the solution is. So the solution is essentially uh this disc with a handle is a disk where you identify two pairs of geodessics.

[00:38:53]And so uh we're thinking about the reormalized geodessic length between the two boundaries. What happens is that this this length jumps from a geodessic which intersects the matter operator to the geodessic which doesn't intersect the matter operator. So in the length uh renormalized length effective action this is some quench uh solution where you just quench the potential and uh this part of the geometry where the interaction is completely negligible. The length is just going through the matter operator. Uh it's very similar to the onepoint uh wormhole construction by Douglas and Misha and friends.

[00:39:35]Um so yeah, so one can find what the size of this closed universe is as a function of the conformal dimension of the matter operator and of the coupling.

[00:39:44]There's some nice formula for it.

[00:39:51]It's a circle but you're I'm identifying these two uh trajectories and I'm identifying these two as well. So uh this is like cutting the wormhole longitudinally and this is like this is the a cut that I was drawing before over here over here. So I'm cutting over here and I'm cutting over here.

[00:40:19]Okay. So, uh, how much time do I have?

[00:40:24]Oh, okay. Good. So, maybe I should slow down a little bit then. Um, uh, okay. Let me recap what we did.

[00:40:37]Okay. you're hungry or uh so the the point is that um okay what we did is to provide uh hol well we constructed a state a state of a holographic system which contains a matter in the black hole interior and we cooled it down be below the hawking page transition so the dominant bug saddle jumps from a black hole to a closed universe and uh the space of this closed universe especially disconnects from the ads region.

[00:41:14]However, at finite temperature, there's still the two things are still connected essentially because the state of the quantum fields on on both sides is entangled with each other. So even though there's no geometric connectivity, there's no black hole horizon connecting them together, there's some uh entanglement.

[00:41:34]And so if we want to describe the quantum information of the closed universe from the holographic system, it has to sort of flow through this entanglement.

[00:41:43]Um at least this is how we uh think about how uh we would describe the black hole interior in in ADSFT.

[00:41:52]And so the hilbert space description in this uh external holographic description uh describing this closed universe is some subspace of the holographic hilbert space whose dimension is fixed by e to the sbul where sbalk is the bulk entropy uh between the ads region and the closed universe.

[00:42:15]So let me make some very basic points.

[00:42:18]The holographic description description is very poor when the entanglement entropy between the closed universe and the ads region is order one. And uh that's definitely true. Essentially we have only a few states over here. Uh and there's a a large effective field theory uh hilbert space in the closed universe.

[00:42:38]So this holographic description becomes better if we scale the bulk entanglement with them. And uh in particular uh in higher dimensional ads there's a way to do this. Essentially the point is that you can have a gas of particles in higher dimensional ads which is a stable microcononically up to very high energy.

[00:43:00]So you can in principle use this high energetic gas which is stable to entangle it uh to this closed universe.

[00:43:13]Yes.

[00:43:21]>> No. So yeah. Yes. No, I didn't say that.

[00:43:24]In higher dimensions, the point is that if you follow this thermal phase transition, the bulk entropy below the hawking page transition is order one.

[00:43:34]And so you would have order one like an EPR pair connecting them together. So >> yeah.

[00:43:46]Yes.

[00:43:54]Yes. So the the goal will be to find an explicit map between the what happens here and the SYK model. Uh we didn't do that. Uh but uh no at this time presenting the model and uh then we yes uh but the point is I was trying to make here is that we know already that if the entanglement is very low the map is going to be very bad. So essentially you won't be able to distinguish what's going on here because all of the quantum information here has to flow through this entanglement. So states which are orthogonal here will look totally parallel in the holographic hill space.

[00:44:37]>> No it's the is this yk model. Yes. Um okay my point here is that you can scale this entanglement within in higher dimensions. Here you don't in in the maldeny setup you don't need to do that because the low temperature thermal entropy is already order n at finite temperature. So essentially the point is that there's order n bulk fields in the bug dual to syk which are of the same mass here and so even if you go to the low temperature phase where there's there's supposed to be this closed universe here uh these uh fields are excited at finite temperature and so uh this kind of entanglement is of is of order n uh in that model and in particular there's something more interesting in this model which is that microcononically this closed universe phase is and the black hole phase they are connected by a smooth crossover. So even if there's a high temperature thermal phase transition microcononically there's a smooth crossover. Um so microcononically these two phases are totally indistinguishable. There should be a smooth transition. Yes.

[00:45:48]>> Yes. Yes. I guess what you can do like in higher dimensions our idea was the following. You started with a thermal state at low temperatures. You have order one uh staff order one entanglement and then you insert matter operators in the uklidian preparation.

[00:46:05]So this these matter operators they won't increase the temperature. They will just inject some energy and their wave function will be spread throughout the two uh parts of the spaceime. So they will increase the entanglement entropy. So this is literally like adding an EPR pair by hand on top of a low temperature thermal state and uh higher dimensions in principle you can do that up to very high energies.

[00:46:39]have a large spread.

[00:46:42]>> Well, if the particle that you're inserting has a definite mass say or the one mass, it will >> Yeah.

[00:46:52]>> Yeah. Yeah. But it will be a microcononical version. This is different than to increasing the temperature.

[00:46:58]It's very different. Uh yeah, we can we can chat about this. Um, okay. So, good.

[00:47:10]Uh, so let me just make a a comment about how this holographic map is supposed to work. So, we have a in the back we have an ads region which is entangled with this closed universe.

[00:47:23]In the boundary, we have a pure micro state. So, there seems to be sort of a some tension between the fact that the boundary description is a pure state.

[00:47:31]there's no entropy entanglement entropy while on the other hand the ads region is entangled with something else. So the point is that the way the quantum information in the closed universe is supposed to be described by the boundary is through this holographic map which is a projection to a single closed universe space. So here I'm representing some entangle state of the quantum fields between the closed universe and the ads region.

[00:47:59]uh what I'm saying is that we know what this state is because we know what the bug saddle is and we know how to what bug state this uh battle prepares.

[00:48:09]We know what the boundary micro state is. So we know what the map between the two is and the map turns out to be a projection into a single uh closed universe state. So all the quantum information of the closed universe gets projected into single into this single stage and uh well this is very confusing uh for many reasons like there's no clear uh physical interpretation of what this projection means I think uh but uh let me just make some quantitative points which is that we can study this closed universe sort of precisely in SYK. essentially we know how to define it and we can uh numerically explore it at a small n for example. So one property which is expected from this state is that this state is supposed to be very erratic. It's supposed to depend very erratically on the precise uh microscopics of the heavy operator that's that stabilizes the closed universe.

[00:49:10]Uh actually we had a talk yesterday about this eraticity of heavy operator matrix elements. So it's related to to the raticity of this wave function. So one thing we can do in SYK is we we can just plot uh this wave function numerically and we can corroborate that at least as a function of the SYK couplings uh this closed universe state to which all the quantum information gets projected looks like a random state.

[00:49:38]uh in higher dimensions. This is a hypothesis about for example uh the structure of OP coefficients and so on for a holographic safety. Here we can just plot the matrix elements of a heavy operator and uh which are related to the uh wave function components of this closed universe state. With this I just wanted to say that SYK seems like a promising arena to to understand these uh erraticity issues uh better.

[00:50:07]And uh let me end with some open questions that I'm not going to discuss uh today uh but which have been discussed in the literature around this uh uh closed universe story. So well my main question that that I would like to understand better is what this uh projection to a single closed universe state is doing physically. So it seems that at least within the semi-class picture of a closed universe entangled to ads that shouldn't be the full description for a pure CTF micro stage. So this projection should be doing something and this something should also be doing uh should also be important to describe the black hole interior. Okay.

[00:50:51]Now if we just take the average over the heavy operator, this projection essentially does nothing and we recover the naive semiclassical picture of the closed universe. And so there seems to be uh an ongoing discussion about whether this average is really necessary or whether the closed universe is there for a single micro state of the of the holographic system which by the way given this construction should also apply for a black hole interior.

[00:51:22]Um so yeah this is at well in my talk I focus on an approach which is sort of extrinsic. I've entangled my closed universe to some external ads region and I'm trying to describe this closed universe from the exterior. But there's another approach which I think is perhaps more promising which is to try to formulate an intrinsic uh non-perturbative Hilbert space for for the closed universe and this has been uh attempted by uh different groups uh given uh a modification of the conventional rules of the gravitational path integral. But uh I think an open question in all of this story is whether there is a microscopic description of these uh of these rules or of this observer.

[00:52:05]And I just want to say that SYK looks like an interesting arena to explore these ideas because the starting point is a simple quantum system where the disorder is defined in the couplings and one should be able to understand all these issues better. And with this I want to end uh my talk. Thank you.

[00:52:40]Yes.

[00:52:44]Yes. Yes.

[00:52:50]Yes.

[00:52:51]Yes.

[00:52:54]Yes, exactly.

[00:53:01]Yes.

[00:53:04]Well, well, there there have actually been uh at least bottom up construction of this malathnachi story in ADS3 uh by Christian Jensen and friends. Uh so essentially there the idea is that you couple the the boundary graviton theory of two boundaries this alles theory with a bunch of Wilson lines and there's some effective potential which modifies the the theory and there's an eternal traversible wormhole version in 3D u but uh I guess so yeah in high dimensions it would be it would be like explicitely a coupling uh by some bill operator uh >> yeah already >> you mean yeah you >> you don't have to I was just saying that there this story I guess could be also done in higher dimensions but yeah the coupling is not totally necessary in higher dimensions because you already have this thermal phase transition in higher dimension Well, I guess the puzzle is everywhere.

[00:54:23]Uh yeah. Uh so you're you're worried that if we understand this model, we might not be learning anything about higher dimensions. Uh I don't know. Maybe.

[00:54:42]Yeah.

[00:54:43]>> So what understood.

[00:54:47]>> Yeah.

[00:54:50]>> Yeah.

[00:54:52]>> Yes. Yeah.

[00:54:59]>> Yeah.

[00:55:01]>> Yes.

[00:55:03]Yes. Well, the variance is large, but uh the point is whether that means uh anything. You can have a random state of a gas of particles in ads and the variance is large depending on what which random state you pick but it is it is just a r a gas of particles in ads.

[00:55:21]So yeah the I think the big question is whether for a single instantiation of let's say the couplings and the operator this closed universe is there or not.

[00:55:28]That's the big question that I think hasn't been uh solved. Well at least I haven't said anything about it. Yeah, what is definitely true is that if you average then this closed universe emerges.

[00:55:47]>> Yes.

[00:55:49]>> Yes.

[00:55:51]>> Yeah.

[00:55:52]>> So it's like a this is one component as a function of the SYK couplings. This is a histogram. So it's like a gausian random uh state.

[00:56:03]the right here.

[00:56:04]>> Well, yeah, I'm giving you different couplings and uh I'm plotting one component of this stage.

[00:56:13]Uh so for a sing you give me the couplings and this is one point over here. If you change the coupling slightly, it will just move around. It's some random uh gausian distribution.

[00:56:26]>> Well, this is the gausian distribution as a function of the couplings. If you change the couplings, you land on a different point on this distribution.

[00:56:37]Yes. Exactly.

[00:56:38]>> Exactly. Yeah. Yeah. Like for example, the face whether it's positive or negative. Uh well in this case this component is real. So it's a real gausian. So that is a binomial.

[00:56:50]>> Yes.

[00:56:52]>> It is sort of symmetric the histogram.

[00:56:55]So it's sort of a binomial distribution whether it's positive or negative with the same probability.

[00:57:03]Yeah.

[00:57:14]>> Yes.

[00:57:21]>> Yeah.

[00:57:26]Yeah. Yeah.

[00:57:36]Uh you mean so you are you worried about uh yeah I guess I guess it depends on how you define your code subace what I was doing I was thinking about is to fix so divide this leg into two sort of purify the closed universe and uh fix this entanglement. So that's my code of space. I can I'm not allowed to touch uh to modify the entanglement to the closed universe and I can just input any other state for the rest of the fields.

[00:58:22]Yes. To the Yeah. And that shouldn't depend on whether this kind of connection is just bulk entanglement or uh geometric connectivity in the case of the black hole if it's order to some power. I guess um yes.

[00:58:43]Yeah. Yeah, I guess you're asking a more interesting question, which is what happens if you're allowed to disconnect this closed universe and then this holographic description is like uh goes wrong.

[00:58:56]Yeah, >> thank you.