Quantum Entropy Function from AdS(2)/CFT(1) Correspondence

Abstract

We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS_2/CFT_1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of string theory on the near horizon geometry, -- named the quantum entropy function. In the classical limit this reduces to the usual relation between statistical entropy and Wald entropy.

LaTeX file, 27 pages, A modified and extended version of the talk given at Strings 2008

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• Lectures on Quantum Black Holes
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• Nonperturbative black hole entropy and Kloosterman sums
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• Lectures on AdS Black Holes, Holography and Localization
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• Menagerie of AdS${}_2$ boundary conditions
• Extremal and Near-Extremal Black Holes and Near-$CF{T}_1$
• Black hole entropy in massive Type IIA
• A fixed point formula for the index of multi-centered N=2 black holes
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• All solutions of the localization equations for N=2 quantum black hole entropy
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• New boundary conditions for AdS${}_2$
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• How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?
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• Black Hole Hair Removal: Non-linear Analysis
• Hairy Black Holes and Duality in an Extended Supergravity Model
• A Twist in the Dyon Partition Function
• BRST quantization and equivariant cohomology: localization with asymptotic boundaries
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• Anti-de Sitter holography for gravity and higher spin theories in two dimensions
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• Twisting and localization in supergravity: equivariant cohomology of BPS black holes
• Quantum Corrections to Supergravity on AdS${}_2\times S^2$
• Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity
• Near the horizon of 5D black rings
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• Partition Functions in Even Dimensional AdS via Quasinormal Mode Methods
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