## Sunday, October 16, 2005

### Black Hole Attractors and Entropy

On Friday, Atish Dabholkar from the Tata Institute of Fundamental Research, visited Imperial to talk about microscopic entropy counts, small black holes and the use of the attractor mechanism. This is a very interesting topic, and arguably the area where string theory has had its greatest success so far.

But what about that NS string we considered alone earlier, our arguments told us that it had zero entropy, and yet it still contains microscopic degrees of freedom, so what's going on? Atish Dabholkar started his talk by asking us whether the S(Q)=klog[\Omega(Q)] was absolutely correct and if we could compute corrections to both the macroscopic and microscopic counts of the form:

S=a_0A(Q)+a_1log[A(Q)]+a_2/A(Q)+....
klog[\Omega(Q)]=b_0A(Q)+b_1log[A(Q)]+b_2/A(Q)+....

He pondered whether we could compute the a's and the b's and did they agree, and then told us that for a class of BPS N=4, D=4 black holes this can be confirmed. He said that on the macroscopic side one must take into account higher derivative corrections to the action (i.e. graviton scattering) and work in the thermodynamic limit for the association between entropy and degrees of freedom to carried over exactly from statistical mechanics. If this approach is sensible, then we would find that our NS string would have contributions to the entropy but not at the first order.

Atish outlined his approach, or ingredients as he put it:

1. Action: N=2 sugra + topological string
2. Entropy: Bekenstein-Hawking-Wald formula
3. Solution: via the Attractor mechanism
4. An ensemble: some Ooguri-Strominger-Vafa mix of charges

He told us he would work with small black holes (= only two charges in the ensemble), where the counting can be done exactly and the classical area vanishes (as we saw above), and so corrections are essential. The approach is detailed in his 4-page paper Exact Counting of Black Hole Microstates and in his talk he commenced by telling us about how to regularise black hole backgrounds by using "stringy cloaks" and this is described in his 10-page paper with Renata Kallosh and Alexander Maloney entitled A Stringy Cloak for a Classical Singularity (you can watch a talk by Andrew Maloney on this paper here). Since the details of the talk are not suitable for blogging I will direct the interested reader to the other relevant and much longer papers written with Frederik Denef, Gregory W. Moore and Boris Pioline, the 35-page Exact and Asymptotic Degeneracies of Small Black Holes and the 103-page Precision Counting of Small Black Holes. Also of interest will be Ashoke Sen's Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity, and you can see the slides and listen to a related talk given by Sen here.

Sorry to trail off without describing the details but one they are tough, and two I am tired. All comments on this approach and joyous sonnets praising (and explaining)the usefulness of the attractor mechanism are welcome. There, and I didn't even mention supersymmetry once, oops.

Update: Check out Jacques Distler's post about David Shih's work on Ooguri-Vafa-Strominger constructions and see also his comments on Dabholkar et al's work and small black holes.

Plato said...

Wow!, lots to think about and digest here.....where does one really begin ?:)

P.P. Cook said...

Sorry, I got carried away - I didn't even make nice paragraphs so it could be read easily, oh dear. However I think the golden rule should be: begin with Zwiebach!

Best wishes and apologies,
Paul

Plato said...

No No, your assessment is very good and link orientated to help perspective.

It was a deeper philosophical question about "emergent spacetime phenomena" that Lubos might be refering?

Yes of course to your point about Zwiebach. No question in terms of model assumption, but if each were to grab a "part of the elephant" and all are trying to describe some aspect of reality, then maybe there are indeed all questioning the same thing? Just from different avenues.

I'll give link on "elephant" shortly.

Plato said...

Six Men and the Elephant

My link to Lubos in post above, has a link to this question of "emergence." Laughlin does not like this term? He call's it, "bricks or seargent majors"

So when the question of where this beginning is, we have to assume that string theory is much closer in this discritpion?

You need some "reference" and your blog entry here is helping from a layman perspective in that orientation, I believe.

I liked your "optiverse link," as I have much to say about this visualization technique to help me see what you are doing topologically. I have much to learn here.

P.P. Cook said...

Don't we all... :)

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