## Wednesday, February 07, 2007

### Iosif Bena: black hole microstates

Iosif Bena was so nice to give us a special, informal talk about black hole and black ring microstates. If you combine black holes and black rings, you can obtain black Saturns as Henriette Elvang et al. call it, but Bena et al. don't want to combine them in the same configuration. ;-)

There has been some tension between Harvard led by Andy on one side and Iosif, apparently representing the consensus of 90% of the rest of the world ;-), on the other side concerning the meaning of the word "microstate" etc.

A state is a wavefunction (or wave functional) on the configuration space of your theory, not a classical configuration as the consensus seems to think. ;-)

Iosif uses the word "microstate" for particular classical configurations which is hard to digest. But if you remove the controversial terminology from his message and if you try to make sense out of what he said, the result is that they can apparently construct stationary spherically asymmetric solutions of the supergravity equations that look like the D1-D5-P and similar black holes almost everywhere outside the region where you would normally expect an event horizon. These solutions are supported by fluxes and they have bubbles in them. The fluxes are adjusted to make the configuration completely smooth, as you can check by a change of coordinates. These solutions may be viewed as uplifts of Denef's solutions. See e.g. Werner+Bena
They can also calculate the redshift at the point where the bubbles start, translate it into a mass gap via the AdS/CFT dictionary to see that it agrees with the mass gap of some string states on the CFT side, and they argue that their "states" (classical configurations) should thus be generic and account for all of the black hole entropy. I think that it is fair to say that no one at Harvard understands these arguments, to use a polite language.

Why do they think that their list of degrees of freedom used for their supergravity solutions is complete? The Schwarzschild solution is also a generic solution that looks like a neutral black hole everywhere outside the event horizon: does it mean that the (zero-dimensional) space of such solutions has a volume that corresponds to the exponentiated entropy?

At any rate, we have already mentioned Samir Mathur's picture that these solutions don't contradict the no-hair theorems because several conditions of the no-hair theorem are not satisfied here. This framework would give a completely new picture of physics inside the black holes. For example, you would probably get killed as soon as you would approach the former horizon.

#### 1 comment:

1. Hi Lubos,

First, I think the correspondence between string theory in a certain asymptotically AdS geometry and the dual boundary theory in a certain vacuum or state is a
feature of the AdS-CFT correspondence. One can compute an infinte set of one-point functions in a certain bulk geometry, and map those exactly to the expectation values of the corresponding operators in the dual CFT state, This state is usually a superposition of the eigenstates of the CFT (see for example hep-th/0611171 or hep-th/0607222
where such dictionary has been worked out in rather gory detail).

A few other examples where asymptotically AdS bulk geometries or configurations are mapped to states or vacua of the dual boundary theory include:

- Giant Gravitons and the Lin-Lunin-Maldacena solutions (hep-th/0409174)

- the Polchinski-Strassler string dual of the N=1* theory (hep-th/0003136)

- The D1-D5 system (see for example Lunin and Mathur hep-th/0109154, or Lunin Maldacena and Maoz hep-th/0212210).

I'm also not aware of any asymptotically AdS solutions that were argued to be dual to anything else but states or vacua of the boundary theory :-)

The second point is that our solutions have a translational U(1) symmetry, which makes them quite rigid. Accordingly, we never claimed our configurations will be dual to ALL the black hole microstates. We argued (based on the mass-gap) that our geometries are dual to some states on the boundary that belong to the same CFT sector as the CFT typical states. Moreover, if some of the states in the "typical sector" of the CFT are dual to horizon-less smooth configuration, it is highly unlikely from a CFT perspective that other states in this sector will be dual to something with a horizon. It is much more plausible that all the typical CFT states are dual to horizonlss configurations.

Of course, this argument for Mathur's proposal is indirect, but is the best we can give at this point. I would of course love to be able to construct the full moduli space of such solutions and configurations (like in LLM or in the D1-D5 case), count them and see if there are enough to reproduce the black hole entropy. Nevertheless, even finding one solution that corresponds to a 5D black hole with large entropy has been rather
challenging; hence it will take people working on this programme a bit more time before reaching that goal.

All the best

Iosif Bena