Three Lectures on AdS/CFT

MSU postdoc Steve Avery explains AdS/CFT to non-specialists (i.e., theoretical physicists who do not primarily work on string theory / quantum gravity). Steve is applying for faculty positions this fall -- hire him! :-)

AdS/CFT on this blog. See also Entanglement and fast thermalization in heavy ion collisions: application of AdS/CFT to collisions of heavy ions suggests that rapid thermalization occurs there due to quantum entanglement.

As an example of the versatility of theoreticians, Steve has also been working with me on machine learning and genomic prediction. He just wrote a very fast LASSO implementation in Julia that includes some automated capability to set L1 penalization and detect phase boundaries.

White holes, entropy and comments for Lubos

Lubos Motl doesn't like my recent paper (arXiv:1007.2934) on white holes. Lubos is a very smart guy, so I take his remarks seriously.

Before getting to his comments, let me say a few things about what I did in the paper.

A. The "white hole" I analyzed is just a classical background which is the time reversal of (part of) a black hole spacetime. The initial data for this spacetime can be obtained from a spacelike slice across the usual black hole spacetime ("after" the horizon has formed), and need not include the singularity.

B. I imposed the condition of isolation (vacuum) outside the white hole at early times. This is equivalent to requiring no radiation in the future of the original black hole spacetime. An unusual boundary condition, but corresponds to the "isolated" white hole I was interested in investigating.

C. I used Hawking's method (i.e., Bogoliubov transformation of in- and out- modes) to study the future behavior of the white hole, or, equivalently, the initial preparation of the black hole required to prevent it from radiating.

It should be clear from the summary that my paper can be read as merely analyzing the black hole spacetime with a nonstandard future boundary condition and then interpreting the results in time reversed language. ("Look ma, no white hole"!) That is, the methods I use have exact time reversal invariance built in. In the paper I note that an isolated white hole and an isolated black hole behave differently. That is not a violation of time reversal invariance applied to an entire spacelike slice because the time reversal of an isolated black hole (which radiates into its future) is not an isolated white hole -- rather, it is a white hole bathed in incoming radiation (from its past) at the Hawking temperature (see figures in the paper). However it does contradict the idea that the time reversed evolution of the hole can be understood independently of its environment (i.e., what is outside its horizon).


Lubos makes a number of remarks in his blog post. I try to summarize them below, together with my comments. He may make other claims as well that I haven't addressed.

1. We know from string theory that black holes and white holes are the same thing. Well, let me first point out that not everyone believes in string theory as the correct theory of quantum gravity (i.e., describing our universe) at 99.9 percent confidence level. Secondly, if a semi-classical calculation like mine suggests differences between the behavior of an isolated white hole and an isolated black hole, isn't it interesting to reconcile that with what AdS/CFT predicts? Although I am not an expert on AdS/CFT I suspect that the time reversal invariance of the CFT boundary state only implies time reversal of the entire bulk state (i.e., on an entire spacelike slice) and not of the black hole alone. If so, there is no contradiction with my results -- see above. Perhaps someone can clarify this for me?

2. Hawking clearly said the same in his 1976 paper. That was my impression on first reading, but since all of his arguments center on the case of a black hole in equilibrium with a bath at equal temperature, it is unclear (at least to me) how this can be generalized to an isolated white hole. That was one motivation for my investigation.

3. Entropic arguments imply that white holes (as obtained via (A) above) are extremely unlikely: specifically, a highly entropic white hole should not explode into lower entropy ejecta. I understand the argument but don't place as much confidence in it as Lubos does. The uncertainty is not about the 2nd Law but about the interpretation of black or white hole entropy.

Lubos does not want me to consider classical spacetimes generated by the initial data obtained in (A) above. Even if one accepts that such spacetimes are highly improbable, that does not mean that they shouldn't be studied. (For example, if you are a many worlder there are some branches on which exploding white holes are observed!) Apparently it is in bad taste to think about (exploding) white holes, but perhaps Lubos should tell this to, e.g., Frolov and Novikov.

Now, a little analysis of the cognitive dissonance (conflicting priors ;-) between Lubos and me. When I say "white hole" I mean the time reversal of some classical black hole spacetime. I consider this (time reversed) spacetime of theoretical interest, even if it results from strange initial conditions. I use what I know (general relativity + quantum fields in slightly curved space) to probe the more mysterious issues (black hole entropy, quantum gravity, ... ). This follows Wheeler's approach of "radical conservatism" -- take the physics you trust with high confidence, and extrapolate to extreme conditions until something interesting happens! Lubos is a true believer in string theory, so to him a black hole is this stringy thing about which we already know almost everything, including that its entropy is due to countable internal microstates, it is dual to some YM configuration through holography, etc. This will likely elicit a shriek of anger from Lubos (or he will just call me dumb), but I consider all of those claims plausible but perhaps not true in our universe: string theory may turn out not to describe Nature.


Finally, there is also some discussion of my paper here and here, but it seems that both authors are slightly confused about the results (perhaps this is my fault for not being clear :-). For example, the requirement that white holes "explode" is not a consequence of my analysis, but just follows from time reversal of the black hole formation event (see, e.g., Frolov and Novikov or figures in the paper). I am only studying the quantum effects (i.e., equivalent of Hawking radiation), which are a correction to the classical evolution.

Further discussion in a follow up post about white/black hole entropy.

Heretics in the church: black hole information loss

Bob Wald gave a nice talk from the "relativist perspective" at the KITP workshop on firewalls -- see Fri Aug 23 3 PM ; slides. (@36 min things heat up a bit :-)

One of the ideas that he and Bill Unruh have advocated over the years is that decoherence is an example of pure to mixed state evolution that doesn't require catastrophic side-effects like energy non-conservation (Banks, Peskin, Susskind; B-S interchange with Wald @42min :-). For related discussion, see these papers: BHs and spacetime topology, BHs and decoherence and this talk from an earlier KITP workshop by Bill Unruh.

Bob also takes some shots at the church of AdS/CFT, pointing out that the duality is not well-defined and still a conjecture. If AdS/CFT is the strongest argument in favor of purity of BH evaporation, then one should not abandon alternatives just yet ... (@53min some further discussion of this which unfortunately cuts off just as Maldacena is giving an interesting argument!)

Monsters in AdS

Slides I used for the workshop discussion yesterday: What Part of the Asymptotically AdS Gravitational Phase Space is Dual to a CFT?

In classical general relativity one can construct configurations with fixed ADM mass but arbitrarily large entropy. These objects collapse into black holes but have more entropy than the area of the resulting black hole. Their interpretation in quantum gravity and in the AdS/CFT duality is an open question.

This topic is also nicely discussed by Don Marolf here and here.

It was great to have Bill Unruh in the audience, whom I had never met in person before.

Miami 2007: 10 years of AdS/CFT

I found this tag and notes when I sat down for the afternoon session :-)

Miami micro-climate is killing me: outside it's 80 and humid (with small rainstorms rolling through), but indoor temperatures seem to vary from 60-70 degrees! Sometimes I'm shivering under blasts of cold air in the lecture hall -- I've discovered you have to carry a jacket around with you all the time just in case the AC is on overkill.

Monsters in Modern Physics Letters

My student David Reeb and I were asked to write a short review of our recent work on monsters for the journal Modern Physics Letters. The review is now on arxiv. You can find slides from a recent talk on this subject here (given at Fermilab).

We included some new material in the second part of the paper. In the last few years there has been significant progress in the foundations of statistical mechanics, in which thermodynamic properties are seen to emerge as a consequence of entanglement and the high dimensionality of Hilbert space. Even the Second Law can be deduced in a probabilistic sense from underlying dynamics that is fundamentally time-symmetric. We discuss the possibility that a similar approach can be applied in gravity to deduce, e.g., the Generalized Second Law of Thermodynamics, which governs black hole entropy as well as that of ordinary matter.

Monsters, black holes and the statistical mechanics of gravity

Authors: Stephen D. H. Hsu, David Reeb

http://arxiv.org/abs/0908.1265

Abstract: We review the construction of monsters in classical general relativity. Monsters have finite ADM mass and surface area, but potentially unbounded entropy. From the curved space perspective they are objects with large proper volume that can be glued on to an asymptotically flat space. At no point is the curvature or energy density required to be large in Planck units, and quantum gravitational effects are, in the conventional effective field theory framework, small everywhere. Since they can have more entropy than a black hole of equal mass, monsters are problematic for certain interpretations of black hole entropy and the AdS/CFT duality.

In the second part of the paper we review recent developments in the foundations of statistical mechanics which make use of properties of high-dimensional (Hilbert) spaces. These results primarily depend on kinematics -- essentially, the geometry of Hilbert space -- and are relatively insensitive to dynamics. We discuss how this approach might be adopted as a basis for the statistical mechanics of gravity. Interestingly, monsters and other highly entropic configurations play an important role.

Excerpt from the paper:

Can the quantum mechanical derivation of statistical mechanics given above be applied to gravity? For example, can we deduce the Second Law of Thermodynamics on semiclassical spacetimes (i.e., including, for example, large black holes)?

This might seem overly ambitious since we currently lack a theory of quantum gravity. However, the results described above are primarily a consequence of the high-dimensional character of Hilbert spaces. If the state space of quantum gravity continues to be described by something like a Hilbert space, then its dimensionality will almost certainly be large, even for systems of modest size. Further, it seems a less formidable task to characterize some aspects of the state space of quantum gravity than to fully understand its dynamics. Indeed, for our purposes here we only consider semiclassical spacetimes.

Early attempts at quantization, culminating in the Wheeler-DeWitt equation, were based on the classical Hamiltonian formulation of general relativity\cite{WDW1,WDW2}. These led to a configuration space (``superspace'') of 3-geometries, modulo diffeomorphisms, and to the wavefunction, $\Psi [ h_{ab}, \phi ]$, of the universe as a functional over 3-metrics $h_{ab}$ and matter fields $\phi$. This description of the state space seems quite plausible, at least in a coarse grained sense, even if the fundamental objects of the underlying theory are something else (strings, loops, etc.). Let us assume that some form of short-distance regulator is in place (or, alternatively, that the dynamics itself generates such a regulator in the form of a minimum spacetime interval), so that we can neglect ultraviolet divergences.

Now consider the set of asymptotically flat, non-compact 3-geometries. Impose conditions on the asymptotic behavior so that the total ADM mass of the system is $M$, and further assume that all the energy density is confined to a region of surface area $A$. This results in a restricted state space ${\cal H}_R$. If the concentration of measure results apply to ${\cal H}_R$, then the observed properties of any small subsystem $X$ are likely to be the same as if the universe were in the equiprobable, maximally mixed state $\rho_* = \mathbbm{1}_R / d_R$. In the flat space case this leads to the usual canonical (Boltzmann) distribution in $X$. ...

Big brains battle black hole firewalls

When I gave an informal whiteboard talk on this topic at IQIM I remarked that after almost 30 years (Hawking first proposed that black holes destroy quantum information in 1974), theorists are still baffled by the black hole information paradox.

Three recent blog posts on the information problem and firewalls:

Scott Aaronson (see lively discussion),  John Preskill (I stole the picture from John), Lubos Motl (I think Lubos has the physics right in his post but I would probably more polite to our colleagues about it  ;-)

Earlier post on this blog. My recent paper -- see eqns (3)-(5) for discussion of density matrix similar to Motl's. Like Lubos and Preskill (and everyone else?), I was never convinced by Hawking's concession paper on the unitarity question, but I do acknowledge some similarities between his arguments and mine.

Finally, in recent discussions with Samir Mathur I became aware of his paper What the information paradox is not, which I recommend. (See especially the section on AdS/CFT.)

Perimeter talk: monsters

I'm traveling today to the Perimeter Institute in icy Canada. I love modern architecture -- can't wait to see their funky building.

[Video and audio of seminar available here -- I'm always afraid to listen to or watch myself giving a talk, but I should probably do so at some point to improve my presentations...]

Curved space, monsters and black hole entropy

slides

Abstract: I discuss a class of compact objects ("monsters") with more entropy than a black hole of the same ADM mass. Such objects are problematic for AdS/CFT duality and the conventional interpretation of black hole entropy as counting of microstates. Nevertheless, monster initial data can be constructed in semi-classical general relativity without requiring large curvatures or energy densities.

Paris conference on black hole information

Gravitational Scattering, Black Holes and the Information Paradox, May 26 - 28, 2008.

Web page here. My slides (pdf).

This is quite a good meeting so far. The atmosphere is informal, with about 50 participants.

Today there were two sessions. The conveners arranged brief talks to stimulate discussion, but the format was mostly open. In the early session the scheduled speakers were Giddings, Hawking, Andy Strominger and me. Hawking ended up not speaking, although he was in attendance. In the second session we had Gary Horowitz, Erik Verlinde and Strominger again.

10h 00 - 13h
What is the BH information paradox/problem/puzzle/question?
convener: T. Jacobson

14h 30 - 18h
Is string theory providing a statistical-mechanics interpretation of BH thermodynamics?
convener: J. Maldacena

I thought my talk went well, but I evidently did not convince either Giddings or Strominger that information loss to baby universes is a viable solution to the information problem :-(

There were a number of interesting exchanges. One in particular between 'tHooft, Maldacena, Englert, Giddings and Hawking lasted for some time. The issue was whether gravitational interactions between infalling particles and pre-Hawking radiation states are strong. 'tHooft maintained steadfastly that they are, with support from Englert. I couldn't quite tell what Hawking's opinion was, and all the others were opposed.

The remaining schedule is as follows.


Tuesday 27/05

10h 00 - 13h
Do quantum BH microstates have something to do with a classical geometry?
convener: D. Amati

14h 30 - 18h
Can the AdS/CFT correspondence teach us how to solve the information paradox?
convener: J. Polchinski


Wednesday 28/05

10h 00 - 13h
What can we learn from the study of transplanckian-energy collisions?
convener: G. Veneziano

14h 30 - 18h
BH and workshop evaporation: did we gain any new information?
convener: TBA

Still in Sicily

The Erice meeting has ended, but I'm still here for a couple of days. Yesterday I rented a car with two colleagues and drove to Agrigento to see some impressive Greek temples and have a traditional Sicilian seafood dinner. Now I'm back in the mountains trying to understand some things about AdS/CFT duality.

My collaborator Xavier Calmet won a prize for best theoretical presentation (students and postdocs were allowed to give short talks). I was among the people deciding on prizes, so I was careful not to vote on that one. Xavier's talk was on how a minimal length arises from simple quantum mechanics and general relativity. I think its accessibility was the primary reason for the prize :-)

Although I've been mostly thinking about physics the last week, I've been getting some interesting emails about the deterioration of the US housing market. It seems official data from OFHEO and the census bureau very much understates what is happening. Some of the data showing that we've passed the peak of the bubble are quite dramatic. The next couple of years will be a buyer's market. The open question is of course how the housing collapse will affect the overall economy. It's worth noting that there is a cap on bond returns, since if the economy really tanks, and 10y yields decrease below, say, 4.5 percent, the housing market may reinflate again due to low interest rates. Since 10y yields are currently at 4.8, the maximum capital gain is probably less than 10 percent.