AdS/CFT and non-perturbative gravity in string theory

  • #1


Science Advisor
I understand that suitable compactified strings in AdS correspond to conformal field theories (w/o gravity) living on the boundary space. What I do not get is the exact relationship between non-perturbative gravitational phenomena in the bulk and the CFT.

All what I have seen are perturbative strings living on a certain background w/o any back reaction on this background. So how do I get realistic non-perturbative gravitational processes using AdS/CFT? What is e.g. the framework to describe a gravitational collapse like black hole formation, neutron star merger, cosmological expansion (dS instead of AdS) Brill waves etc. using AdS/CFT? Is there a way to extract non-stationary spacetimes from AdS/CFT in the context of string theory?

Answers and Replies

  • #2
This is a rather speculative paper, but it may reference more standard literature. I've read many times that black holes can form in AdS/CFT.
  • #3
Thanks; I will have a look at the references.

One thing that I forgot to mention: of course even in AdS two things are fixed, namely a) AdS itself (not dS, ...) and b) the five small dimensions. So in a sense it is a tool suitable for a rather restricted (and unrealistic) class of spacetimes only. Whereas AdS can be seen as a superselöction sector the geometry of the small dimensions may also play a role when gravity becomes non-perturbative.
  • #4
If I'm understanding your question correctly, there are lots of papers investigating dynamic phenomena in AdS/CFT by solving Einstein's equations numerically, e.g. People have also put in spinning strings and studied the spectrum of radiation (gravitational radiation in the bulk), e.g. There are other groups doing similar calculations, I just happen to be most familiar with the MIT crowd.

Here is a non-perturbative in strong coupling calculation of decay into an AdS black hole using string world sheet instantons. There are also many studies of perturbative string corrections e.g. Gauss-Bonnet gravity.

Here is a paper showing how a finite N effect appears in AdS/CFT, specifically one is trying to understand the fact that a trace of more than N NxN matrices breaks up into products of smaller traces. The result is a cool picture where branes expand as they move faster and faster similar to the way two opposite charges connected by a spring moving in a magnetic field will also expand. It's ultimately some kind of UV-IR duality, where higher energy things get bigger.

Is this what you had in mind?

PS Although I know people have thought about it, cosmology is IMHO indeed more of a stretch in AdS/CFT.
  • #5
Hi Tom,

you're right to be confused, since, after all the hype AdS/CFT says almost nothing about non-perturbative gravity in the bulk, or, in fact, any potentially natural scenario. In fact I would classify it as pure maths rather than physics.

(Although I'm happier for Maldacena to get $3million bonus than some dumb banker.)

PhysicsMonkey links to some potential results, maybe there is a way forward. I'm sure you are aware of Nastase's 2007 lecture notes, where he discusses possible ways forward in the conclusion
  • #6
Everything in the bulk is in general mapped to the boundary CFT. That includes nonpertubative physics, complete with backreaction and everything else.

Many real physical situations that you can think about in quantum gravity are adequatly described by this correspondance (eg they are expected to work the same in asymptotically flat space), which is why it is so physically useful. Where you run into trouble, is when you have specific issues or problems that require detailed knowledge about the global state of the universe. So unfortunately this precludes some of the more interesting arenas of quantum gravity (like horizon physics and cosmology, which are very sensitive to the global structure of spacetime and wll be significantly different in reality).

Still many problems and situations carry over and will be similar. So for instance while a black hole evaporation is going to be very different process between Ads and flat space, the actual dynamics of the stellar collapse will be much more similar.

Of course, in practise this typically involves a very complicated CFT with highly entangled thermal states, and its very difficult to retranslate back into the bulk language to really give a full story about the gravitational degrees of freedom. But still there is a whole industry of people working on this and similar types of problems.

Amusingly, its often the case that the pertubative physics in the bulk is more interesting than the nonperturbative bulk physics, as knowledge about the former often tells you where and how failure modes appear in the real world. So for instance, its useful to study the perturbative statement regarding Hawking information loss paradox in the context of AdS space, and see how and where it breaks down.
  • #7
But why does eg. say "The absence (so far) of an intrinsic bulk theory at the nonperturbative level appears to impose crucial limitations on our ability to describe black hole interiors and cosmological regions via AdS/CFT, beyond what follows from the approximate methods that were already available to generate bulk evolution."

Does they mean that it is unknown whether AdS/CFT applies beyond black hole horizons, or do they mean it does in principle, but the calculations are too difficult?
  • #8
Well, it depends a little what question you ask.

You see, we don't know what nonperturbative quantum physics in the interior of a black hole looks like in the gravitational language. Consequently we don't have an input to ask what the CFT looks like. Its a bit of a chicken and egg syndrome.

Instead we can start with a generic classical state in the bulk, translate that to the CFT. Then try to evolve the CFT in some way (this is messy and approximate, as anyone who has ever done finite time evolution in field theory knows), and then retranslate back into the gravitational language. So for instance, this is roughly what you would need to do to adequately describe stellar collapse, but of course this is really hard both calculationally and conceptually.

In general, even very simple states like a graviton in the gravitational language are quite complicated objects when translated in the CFT. Its very difficult to 'track' the exact processes which would make what is happening intuitive.

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