I’ve been busy with other things, but after taking a look today at various new things related to quantum gravity, I was struck by how much things have changed sociologically in that subject over the last few years. Back in the days of the “string wars”, debates about quantum gravity were fiercely polarized. Oversimplifying and caricaturing the situation a bit, the two sides of the quantum gravity debate were:

- Those interested in loop quantum gravity as well as other more exotic attempts to reformulate the problem of quantum gravity. These people just considered pure quantum gravity and devoted a lot of effort to analyzing the deep conceptual issues that arise. They sometimes considered highly speculative hypotheses, trying out abandoning the usual basic axioms, for instance replacing fundamental axioms of quantum mechanics. Lee Smolin was an influential figure, and the Perimeter Institute a major center for this research.
- String theorists, who argued that the appearance of spin-two massless mode in the quantized string spectrum showed that string theory was the only way to understand quantum gravity. They claimed that they had a single, very specific and highly technical mathematical structure to study, which obeyed the conventional quantum theory axioms. Their efforts were devoted to specific computations in this theory, and they seemed to regard the other side of the debate as woolly thinkers, caught up in meaningless ill-defined philosophical speculation. The KITP at Santa Barbara, led by David Gross and Joe Polchinski, was a major center for this side of the debate.

These days, things have changed. If you’re at Perimeter, prominent activities include:

- This week’s conference on a very technical issue in string theory, superstring perturbation theory.
- This month’s course of lectures on Explorations in String Theory.
- The next public lecture will feature Amanda Peet promoting string theory. Peet has been one of the more ferocious partisans of the string wars. The text advertising her public talk a few years back at the Center for Inquiry in Toronto warned attendees who might consider “parrotting of critical views by outsiders like Lee Smolin.”

On the other hand, it you’re in Santa Barbara these days, you might be participating in a KITP conference on Quantum Gravity Foundations. This is featuring very little about the technical issues in superstring theory being discussed at Perimeter, but a lot of discussion of deep conceptual issues in quantum gravity. There’s also a lot of willingness to throw out standard axioms of physics, maybe even quantum mechanics. They’re even letting Carlo Rovelli talk.

The sort of speculation going on at the KITP is featured on the cover of this month’s Scientific American, and this week Quanta magazine will be publishing a series of pieces on something related, the “ER=EPR” conjecture. There’s debate whether anyone really understands this and whether it is consistent with standard quantum mechanics. It also features a diagram that people call the “octopus” diagram. Back in the day it was Lee Smolin who was getting grief for an “octopus” diagram (see here), yet another way in which things have changed.

For a more balanced view of quantum gravity issues, you might want to spend your time in France, where the IHES recently hosted an interesting series of surveys of the subject (see here), and the Quantum Gravity in Paris conference featured more specialized talks. In the category of quantum gravity topics I wish I had more time to learn about, Kirill Krasnov’s talk was presumably related to this recent work, which looks intriguing.

I believe that the most natural unification of Einstein gravity and quantum field theory is the (non-perturbative) operator formalism of quantum Einstein gravity. I don’t understand why people wish to neglect this fact.

Peter,

Over the decades, I’ve had similar musings to the firewall and ER=EPR ideas: for example, I remember around 1980 a discussion with Subhash Gupta when we were both at SLAC about the fact that black holes never actually quite form (classically, it takes an infinite amount of coordinate time, but in that amount of coordinate time, Hawking radiation wipes out the black hole); I always assumed something like the firewall had to exist.

But I (and as far as I know Subhash) never got beyond such musings.

So, I hope all this leads to wild successes.

But, my “gut feeling,” alas, is that you have to be Einstein for such qualitative musings to lead to a revolution in understanding.

So, what’s your gut feeling about all this — the firewall, ER=EPR, etc.?

Dave Miller in Sacramento

Dave Miller,

I’ve always been dubious that very general speculation about gravity/space/time/black holes, etc., is going to go anywhere. I tried to give the example of Krasnov’s work as the kind of thing that seems more promising. The big problem of quantum gravity to me seems to be the relation of space-time degrees of freedom and the internal degrees of freedom of the standard model. The best argument for string theory vs. LQG was always that string theory would explain this relation.

These days, prominent string theorists seem to have just given up on the problem, and adopted a version of Smolin’s call for “seers”, but on steroids. The world has always been full of people with ideas about how they are going to revolutionize physics,

ideas which are far too vague and speculative to ever go anywhere. What’s weird is that some of the most prominent figures in the theoretical physics community are now headed down this route (one example of recent years is Verlinde and “entropic” gravity). I’m loathe to specifically criticize “firewalls” or “entangled particles = wormholes” too much since I don’t know exactly what these people are doing (I’ve spent enough time looking at it though to decide that my time was better spent on other things).

One thing that is clear though is that, unless it actually achieves something, putting this on the cover of Scientific American, or otherwise giving it a lot of publicity, is not a great idea. More hype is not what this subject needs.

Peter,

Thanks — I suspect you’re right: perhaps a lot of physicists (and I’m not excluding myself) are overly beguiled by the thought of being Einstein thinking deep thoughts while working in the Swiss Patent Office.

You wrote:

>The big problem of quantum gravity to me seems to be the relation of space-time degrees of freedom and the internal degrees of freedom of the standard model.

Are you acquainted with the “problem of time” in quantum gravity? It seems to me the solution probably lies in an integrated theory where the standard-model degrees of freedom act as “clocks” to make time determinate: of course, I have no idea how to actually do this, alas.

I’ll look into Krasnov’s work as you suggest. Like you, I am old enough to remember when “real” physics meant doing calculations that had, in principle, experimentally testable predictions.

I suppose the best counter-argument to your and my pessimism is that, if enough people muse over various oddities and loose threads in existing theories, perhaps one of them actually will end up being Einstein sitting in the Patent Office.

Anyway, it has been interesting watching the “string wars” and all the rest, even if it is hard to see how it has advanced physics. Thanks for keeping us up to date on what is going on.

Dave

I am glad to see Asymptotic Safety first in the list of alternatives in Nicolai’s survey, rather than at the bottom where it usually is. But perhaps that was just alphabetic. I thought after the remarkable prediction of the Higgs mass by AS, it would have gotten far more attention. Perhaps it is just that non-perturbative theory is so difficult.

The type of ideas discussed by Krasnov, that is GR as YM. have been around for more than 30 years. The classic one is McDowell-Mansouri SO(4,1) gravity, PRL 38, 739 (1977), reformulated by Stelle and West in PRD 21, 1466 (1980) in a way that connects YM with Einstein-Cartan and (anti)de Sitter. Very interesting, but did not lead to anything better than good old GR except for giving a moral raison d’etre for the cosmological constant…

I think that a symptom of what is wrong with string theory right now is that nobody is saying “ER=EPR makes absolutely no sense. It isn’t compatible with our understanding of general relativity, and it isn’t compatible with our understanding of quantum mechanics. Please explain to me how this makes any sense.”

Compare this with the mathematicians’ treatment of Mochizuki’s claim of a proof of the ABC conjecture. Or, if you want a mathematician of the stature of “EP=EPR”, the treatment of Connes’ idea about how to prove the Riemann hypothesis. In these two cases, we get a healthy amount of skepticism.

and then (fast-forwarding a few years) he had to go and learn the then-hardcore-pure-mathematics now known as semi-Riemannian geometry to properly formulate a working theory to get gravity in the picture, with actual predictive power. Having a nice idea like the equivalence principle is not enough.

I hope to hear opinions on the paper by Saini and Stojkovic, Radiation from a Collapsing Object is Manifestly Unitary, PRL114, 111301(2015).

jd,

Bee Hossenfelder has a critical discussion (including some heated back-and-forth in the comments with one of the authors) of the paper.

The bottom line seems to be that:

a) The paper was over-hyped in the media

b) If you assume no singularity forms, the paper proves no information loss occurs

c) Everyone already knew b) anyway

In any case, as I recall, Hawking actually agreed that no information loss occurred some time ago (vide Lenny Susskind’s book), though of course that does not necessarily settle the issue.

My own suspicion is that the horizon never technically forms because of Hawking evaporation (technically, you can only be sure of the horizon at standard coordinate time equals infinity); however, quantum effects should “smear out” the horizon and… well, I’m unclear on how that quantum smearing affects everything.

Dave

@Franck: well, since Connes name has been mentioned in the discussion (in another context though), let me answer that if there is at least one approach where the relation between the space-time degrees of freedom and the standard model degrees of freedom are addressed, this is precisely Connes noncommutative geometry. It can be summarized as saying: the standard model is a gravity theory, but gravity on a slightly non-commutative version of space-time. This is off topic and I already had a long exchange on that topic in the comments of a previous post, so I do not want to discuss it here, just recall that even though it is not hyped in the hep-th community, it exists and has been through recent interesting developments.

Dear Tom,

I partly agree, but there are three important aspects of gravity expressed in connection variables that MacDowell and Mansouri and Kelle and West missed. These are the fact that general relativity in 3+1 dimensions can be understood as a constrained topological field theory and that when doing so there is a redundancy in the equations of motion that can be removed by making the theory depend just on the chiral half of the spacetime connection. That is you can write a topological field theory for the chiral left handed SU(2) left space time connection, and constrain the action in the simplest possible way and find that general relativity emerges.

The third fact is that the action is most directly expressed as a function, not of the metric, and not of the frame fields, but of a self-dual two form. (The constraints that I mentioned yield the frame field as an integration constant.)

When one combines these three insights one has the Plebanski action, (whose Hamiltonian formulation was discovered by Ashtekar), which was also rediscovered by Capovilla, Dell and Jacobson. This action is not just polynomial, it is cubic in the fields, making it the simplest possible action that GR can have. The important work of Kirill Krasnov extends and deepens these insights.

These insights are also at the heart of loop quantum gravity and spin foam models. Non-trivial results are possible for a non-perturbative quantization because the action is that of a diffeomorphism invariant gauge theory with a cubic action, closely related to topological field theory.

Macdowell-Mansouri and Stelle-West build on a different insight, that (in the modern language) you can relate GR to a broken topological field theory of the deSitter or anti-deSitter group. This is compatible with the Plebanski formulation and can be incorporated into it.

Indeed by combining these insights there emerged also a connection with Chern-Simons theory induced in 3 dimensional boundaries such as horizons; and this led to an understanding of the role of the cosmological constant in quantum gravity, as an infrared cutoff that is imposed as a quantum deformation of the chiral SU(2).

Thanks,

Lee

Peter Shor,

I’d be really curious why you think “ER=EPR makes absolutely no sense”. My understanding is that it gives a geometric description of states in QG (very entangled black holes) that had no prior understanding. It is an extension of the AdS/CFT description of the eternal BH/thermofield double, and you can argue for it starting from Ryu-Takanayagi (Section 1 of http://arxiv.org/pdf/1412.8483.pdf). These may not be overwhelming evidence, but why is the idea nonsense?

Dear Lee and Tom,

The Plebanski action is indeed polynomial and cubic, but the action proposed by Krasnov is neither, due to the presence of the square root in the action (2) (also obvious in (20) in his paper). I don’t really see the benefit of this for the spinfoam models. In particular, the absence of the tetrad fields makes it hard to couple fermionic matter later on, just like in the Plebanski case.

There is also the approach based on the Poincare 2-group (I’m shamelessly advertising myself here… see arXiv:1110.4694), with the constrained BFCG action — also polynomial and cubic, similar in structure to Plebanski in that it has a topological sector plus the simplicity constraint. Its advantage is that tetrad fields are explicitly present in the topological sector, which allows for the straightforward coupling of fermions. Also, the constraint has a much more transparent geometric interpretation. Finally, if one adds the cosmological constant term, one can show that the MacDowell-Mansouri action can be recovered as a second-order theory from this action (by substituting one of the algebraic equations of motion back into the action).

IMO, there are many reformulations of GR action in terms of various variables, from the historic ones (Palatini, Einstein-Cartan) to these modern ones (including the teleparallel gravity, both historic models and the recent Baez-Wise version). Each reformulation has certain appeal and benefits, as well as drawbacks. Krasnov’s approach is certainly interesting, but I honestly don’t see why it deserves so much hype. What problem does it solve, that other proposed actions don’t? And is that solution worth the price of the nonpolynomial simplicity constraint?

Best, 🙂

Marko

Well said, Peter Shor. What I find quite entertaining is that Lenny Susskind – who jointly proposed this ER=EPR is obviously completely unconvinced by it and he doesn’t try to hide that very much. I kind of expect him at any moment to say “Oh, I can’t do this anymore. We all know it’s not right.”

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Dear Peter and Lee,

I have read with great joy Peter’s book “Not Even Wrong” as well as Lee’s book “The Trouble with Physics”.

Do you think that this change is a sign that theoretical physics is slowly becoming healthy again (using Lee’s words) and that this will take physics out of its present crisis and lead it back to the exciting and glorious years of the past centuries?

Thanks,

EFT,

Personally I don’t think theoretical physics is getting healthier. The changes in recent years have been a mixed bag. One positive development is that there’s a lot more skepticism in the physics community about string theory, with the issues that Lee and I were raising moving from a marginalized point of view to a rather conventional one among physicists. This potentially creates space for people to work on other ideas. Unfortunately, there has been a backlash against sophisticated mathematical approaches, with too many physicists believing that it was mathematics that led string theorists astray. As a counterpoint, such mathematical research remains alive, partly due to significant funding from Jim Simons.

Among string theorists themselves, a sizable number have basically given up on conventional science, using the multiverse as an excuse to make string theory immune to challenge from experiment. Many if not most have moved on to studying other topics, from condensed matter physics to the kind of quantum gravity going on at the KITP. I have no expertise on the condensed matter stuff, but as indicated here I’m skeptical about the quantum gravity ideas and how they are being pursued. This seems to bring together the worst of the string theory fondness for hype and the worst of the long tradition of empty quasi-philosophical speculation.

@Mark: Why does ER=EPR make no sense to me? Because general relativity is a well-defined theory of gravity without entanglement, and wormholes are created by curved space (possibly with negative energy density), not by information. And because quantum mechanics is a perfectly well-defined theory without general relativity, and entanglement is perfectly well-behaved without invoking wormholes.

@Peter Shor: Thanks for your answer. I don’t think they wanted to explain entanglement or ER bridges, which are well understood. They just say that in QG there are some states (e.g. two very entangled BHs) that can be described in another (dual) way involving an ER bridge. While the original description is certainly fine (the wave function of the two BHs is entangled), the other description they are proposing is more geometrical and may help in calculations/thought experiments.

I’m at risk of repeating myself, but take the most concrete manifestation of EPR=ER: 1. Two CFTs in a thermofield double state. There’s no gravity, but there’s entanglement. 2. Take the eternal BH in AdS, the two asymptotic regions are connected by an ER bridge. By CFT/AdS 1. and 2. are equivalent descriptions of the same thing, so EPR=ER. (I acknowledge that this isn’t a perfect example, because 1. was not a QG state, but I wanted to give a setup, where there are calculations that support the picture.)

@Mark

Let me quote from Maldacena and Susskind’s paper:

And I repeat: with our current understanding of entanglement (which I think is very good), it cannot generate ER bridges, even in the interior of black holes where it’s not falsifiable. You might as well conjecture that unicorns live in the interior of black holes. That’s not falsifiable, either.

To add my own less well-informed take on this to Peter Shor’s, perhaps someone can point me to something I’m missing here (which I surely am):

I understand very well exactly what an entangled pair of particles is, both mathematically and physically. I also understand (less well and less exactly) the AdS/CFT duality conjecture, as a conjecture relating two well-defined theories (supergravity on AdS and N=4 SUSY on the boundary). When people however announce that they are conjecturing some duality between the simple, well-understood entangled particle system and a complicated gravitational system (e.g. a wormhole), I immediately get lost, because I can’t figure out exactly what the gravitational system is or how the mapping is supposed to go. When I try and read about this, all I find are vague general statements about holography and such, so I soon give up.

It’s possible one can get somewhere interesting by following this kind of highly speculative line of thinking, but I don’t see this happening. It seems to me that people are going to credulous people in the press like K.C. Cole to promote vague speculation, long before getting to the point of having a well-defined idea that can be evaluated sensibly in some way or other (of course all of this is completely unmoored from experiment, but it would be nice if it weren’t also unmoored from the parts of theoretical physics we understand).

@Peter Shor

It’s true that using particle scattering you can’t see behind the horizon, so there could well be unicorns there. But people have thought of other (more subtle) observables that probe the interior. Take this paper: http://arxiv.org/pdf/1303.1080.pdf

The time evolution of entanglement entropy after a quantum quench (known in 2d CFT from the work of Calabrese-Cardy) is reproduced by the Ryu-Takanayagi surface going through the ER bridge. (It’s a very special situation, but also concrete. Maybe the same results can be produced without an ER bridge, but the ER bridge is consistent with the field theory knowledge.)

Hong Liu from the CTP also worked on probing the geometry behind the horizon. You can ask him, if you’re unhappy with my imperfect explanations.

The best bit about ER=EPR is that apparently now “a particle is a black hole”. Honestly! Lenny Susskind said it. If a crank had said it, it would have been dismissed.

I can’t say much for the quantum gravity side of things, but I would certainly advocate against a backlash to sophisticated mathematical methods (esp those developed alongside, entangled with the first phase of string theory ending in the 80s) . 1+1-D Conformal field theory has been enormously important in statistical physics and condensed matter; much of this structure grew out of quantum gravity and string-related research. E.g., key results on the structure of affine Lie algebras by Gepner and Witten. 1+1-D CFT underlies the deepest formulations of the fractional quantum Hall effect via Moore and Read’s construction of many-body wavefunctions from conformal blocks, and the understanding of edge states as CFTs (Wen). That’s the clearest application of WZW/Chern-Simons holography to a real well-studied experimental system (5/2 state, which may well harbor non-abelian Ising anyons).

If you are a field theorist working anywhere in quantum physics except unification and quantum gravity, I think you can profitably view much of string theory (1st quantized) as an elaborate self-consistent construction exercised within the framework of conventional quantum field theory. Much of the mathematics that we are now employing in condensed matter has already been field-tested there, and partially translated from the language of mathematicians into a form that one can use to compute things with. I.e. I’m happy to use results from conformal embedding theory, but I’m glad I didn’t have to prove their validity! If string theorists decide to stop doing this job of importing mathematics, I’m afraid us condensed matter theorists will have to do it ourselves. That means more time spent not working on calculations not “immediately” to experiment, or even perhaps concrete models. I’m not sure our funding agencies will approve…

Peter, this is also the first time Ed witten has given a conference (or any technical talk)

at PI. Earlier he has given a public lecture there a decade back

EFT,

Theoretical physics as a whole is pretty healthy, but the subfields concentrating on gravity, high energy particles, and cosmology will remain in their current languid circumstances until more experiments probe those regions, since theorists are impotent and helpless without actual empirical data. This isn’t a cultural problem, since pragmatism will beat idealism if there are good experiments, sooner or later.

Matthew Foster,

Thanks. 1+1 d CFT is an amazing subject, both in terms of mathematics and physics. It’s not really string theory, but string theory research brought a lot of attention and progress to the subject. Unfortunately the CFT in AdS/CFT is a different one, and the concentration of the subject on that topic hasn’t led to the same kind of progress.

gadfly,

Cosmology has lots of data, so does HEP, the problem is that theorists are fond of trying to answer questions not addressed by any data, and often such that it is unclear whether there ever will be data. It’s worth noticing that pure mathematics is a subject that has managed to keep making great progress, even in the absence of any data. Theorists should pay attention to how mathematicians do it. One thing they don’t do is promote ill-defined ideas…

Isn’t that possibility inherent in pure mathematics? It’s not about the physical world and in a strict sense isn’t empirical. The only “data” it might need, if any, are the results of calculations, enumeration of cases, etc., that raise interesting mathematical questions.

Chris W.,

Yes, pure mathematics has always been pursued mostly independent of any data. My point is that mathematicians have over the centuries developed effective ways of making progress based purely on the internal logic of the problems they pursue. This is what theoretical physicists are also trying to do in areas like quantum gravity.

One of the most basic parts of the method of pure mathematics is an insistence that you need to pay close attention to exactly what it is you understand, and exactly what claims you are trying to make. If you don’t, you’ll get lost very quickly. I’ve never had any luck arguing with physicists that if they’re not going to have any data, they need to behave more like mathematicians. In general they’re convinced that making precise statements is a waste of time that will just slow them down, but I think they should give this a try. Couldn’t hurt…

Peter,

I know it is off topic, but April is almost over and I was hoping that you would write a blog entry commemorating the 100th anniversary of Noether’s Theorem which was discovered in April 1915.

Best Wishes

Justin,

Sorry, but I’ve just spent much of the last three years writing a book about how to do symmetry arguments in quantum theory without using Noether’s theorem, for a blog entry about this, see

http://www.math.columbia.edu/~woit/wordpress/?p=7146

So, I’m the wrong person for this.

Noether was a great mathematician, and Noether’s theorem is a great result, central to understanding symmetry in the Lagrangian formalism. But, these days I’m quite wrapped up in the Hamiltonian formalism…

On the issue of quantum gravity/information loss in black holes/firewalls, etc., I just ran across this preprint by Hawking from early last year in which he argues that no event horizon ever actually forms and that therefore there is no need for a “firewall.” The paper has no math at all (!); nonetheless, I am unsure what to make of it.

Peter, I cannot find that you have mentioned this: do you (or anyone else) know what to make of it?

Dave

@ Matthew Foster

Great to know that there is real appreciation for the work of string theorists from a working Condensed Matter physicist. I have seen ego-based nonsense from both sides, but this is rare.

Cool, awesome, etc.

Matthew Foster,

Nobody has denied that the application of CFT to statistical systems is a huge success, and I have argued for 25 years that BPZ deserve a Nobel prize for this. At the same time, the limitation is very obvious in this context.

Since the string world sheet is a unobservable target manifold, in HEP you might argue that infinite conformal symmetry is so special that it must be Nature’s choice. In statphys it is the base manifold that is 2D, and we know that there are 3D systems as well, and that these are both more experimentally relevant and much more complex.

When I was a postdoc I heard a joke about Polyakov’s response to “Good morning”: “Yes, it is a good morning, nobody has solved the 3D Ising model yet”. I have no idea how much truth there is to this joke, though.

@Dave

I expect that even Hawking sees this paper as not an actual resolution of the black hole paradox, but as a proposal for a high-level description of what such a resolution should look like.

Pardon my ignorance, as a mathematician I’m kind of confused by Hawking’s paper. Not the paper, I understand his argument, more or less. And off the top of my head, I’m guessing he’s right about firewalls not existing. But why exactly is ADS/CFT supposed to be useful? I mean ADS/CFT applies in universes with negative cosmological constant, which is not the case in our universe. And it’s only a conjecture. I certainly understand why ADS/CFT is an interesting conjecture, but it seems to me that in order to make it relevant at the very least someone should come up with a version that applies in the actual universe, even if it’s still only a conjecture. Am I missing something?

Jeff M,

This whole story is based on the idea that some version of an AdS/CFT type holography is supposed to explain the black hole information paradox. Ten years ago the people involved in this were claiming that holography solved the black hole information paradox, now they’ve changed their mind, and their arguing about whether/how it does. Part of the problem here is that you don’t know why AdS/CFT holography works, much less how something analogous is supposed to work in this different setup.

Thanks Peter. Personally, I was never really convinced losing unitarity was that big a deal. Not a big fan of determinism 🙂

@Jeff M: I think the big problem with losing unitarity is that we have no idea how to generalize QFT to a reasonable non-unitary theory.

So assuming the real theory is unitary is kind of like looking for your keys under the streetlight. You suspect that the keys aren’t under it, but you also know that if they’re not, you are

nevergoing to find them.Dr. Woit,

I’ve heard Susskind claim that not only does ER=EPR for (maximally

entangled?) black holes, but also for elementary particles. Do you

know what he means by this? How can wormholes connect two entangled

particles if the entangled particles are prepared at low energies?

Thanks.

@ Jeff M

AdS/CFT might be useful and interesting if it helps us say things about CFTs. That’s the context in which there is non-string theory interest in high energy physics, since you could view the gravity dual of N=4 SUSY Yang-Mills as a calculational tool for studying the strong-coupling regime of this theory. How you get from this very special theory to non-conformally invariant standard model physics is not obvious, since the question is how much infrared physics comes in. (And that’s assuming the conjecture works for this special theory). But similar questions arise in connecting lattice models to CFTs and massive integrable QFTs, which do indeed work in suitable contexts. E.g. the E8 spectrum of the massive transverse field Ising model.

Some condensed matter physicists are also interested in AdS/CFT, if it might shed light on CFTs in more than 1 spatial dimension or stat physics models in more than 2D. Without studying the current state of the subject I can’t say much, but my impression is that the precise correspondence is not well-established for other (e.g. non-gauge) theories. Nevertheless, one might hope that some general results about CFTs that do not follow simply from global conformal invariance could be obtained this way, such as the Ryu/Takayanagi formula for entanglement entropy.

One curious aspect of AdS/CFT is that the gravity side at weak coupling is classical and generically non-integrable, meaning you get dissipation (and presumably, chaos and thermalization). One expects these to emerge in an isolated quantum many particle theory when driven far from equilibrium (e.g. following a global quantum quench), so long as the system is not integrable. But in general we don’t know a way to derive such “non-unitarity” from QFT. For disordered quantum systems such as the problem of Anderson (de)localization, we know how to obtain effective non-unitary theories that correctly capture the “chaotic” aspects of such systems, e.g. wavefunction multifractality. These can be non-unitary CFTs, which admittedly are harder to find and make sense of (since they are beyond Peter Shor’s streetlight), but there are a few well-understood examples.

Vladimir,

I have no idea. One problem with this whole subject is that listening to people like Susskind, it’s sometimes very hard to tell the difference between when they have a reasonably well-defined idea and when they don’t, so you don’t know what to ignore and what to pay attention to.

@peter shor. Thanks, nice to know my intuition isn’t completely crazy 😉

@JeffM

In AdS, black holes *still* have the same theoretical problems as in flat space. So it is conceivable that we are not throwing the baby out with the bathwater by working with AdS instead of flat space, even though AdS is possibly substantially more tractable, due to AdS/CFT.

Note also that since the universe is accelerating, real world black holes are not actually flat space black holes either! For astrophysical questions, this doesn’t matter. AdS/CFT deals with fundamental (as opposed to astrophysical) aspects of black holes, and needs the asymptotic boundary in a crucial way, but I think it is still instructive, at least if black hole physics is dominated by the (parametrically at least) near horizon region.

Matthew Foster: Your last paragraph got my attention, could you please provide an entry point to the literature on these non-unitary CFTs relevant to (many-body?) localization?

Thanks,

Moshe Rozali

@ Moshe

The non-unitary CFTs of which I speak describe critical delocalization, as occurs at a non-interacting Anderson metal-insulator transition. There are different examples under different levels of control. E.g.,

1) “Exactly solved” 2D critical states: Dirac fermions coupled to random abelian or non-abelian vector potentials. Critical properties like wavefunction multifractal exponents are known exactly, from 1+1-D CFT. (Non-interacting, so energy is a parameter and the post-disorder-averaged theory is 2+0-D). These are affine Lie algebras, e.g. Sp(2n)_k, U(n)_k, SO(2n)_k. For positive integer n,k these are unitary, but one needs to take the limit n->0 at the end to get results relevant to disorder physics (“replica trick”). There’s a better-defined version (the SUSY trick), but you get the same results. These have also been checked numerically. First papers were by Ludwig, Fisher, Shankar, Grinstein and by Nersesyan, Tsvelik, Wenger in 94. We review these in our recent papers on 3D topological superconductors, since these models turn out to be relevant to surface states.

2) Anderson metal-insulator transition in 2+\epsilon. Perturbative RG results via the epsilon expansion. Same kinds of data can be extracted.

3) Plateau transition of the integer quantum Hall effect. Extensive numerics spanning 20 years, and many indications that the underlying theory is conformally invariant, but no one knows what that theory is yet analytically (as far as I know). Martin Zirnbauer and Ilya Gruzberg are among the people who’ve worked extensively on this problem.

Both 2) and 3) are reviewed in Evers and Mirlin, Anderson Transitions, RMP 2008.

As for the interacting problem (e.g. MBL), obviously I wouldn’t expect space-time conformal invariance because the disorder is non-dynamical. In some situations, however, you can graft interactions into the non-interacting theory and determine stability, and perhaps even identify nearby interacting, critically delocalized fixed points (scale invariant separately both time and space.) This happens e.g. in the unitary metal-insulator transition with long-ranged Coulomb interactions in d = 2 + \epsilon, and also in class AIII topological superconductor surface states in a certain regime (e.g. here).

Thanks Matthew!

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Not strictly on topic, Peter, so delete if you wish, but consider it a request for the future — do you have any thoughts on this stuff? It’s hard for me to tell if it’s the same as the ER=EPR material that was discussed in part I, and which you already addressed in an earlier post. Thanks!

https://www.quantamagazine.org/20150428-how-quantum-pairs-stitch-space-time/

@S: No, that’s not about ER=EPR. It’s about research which is much more plausible than that (that’s not setting a very high bar …).