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Nonperturbative black hole entropy and Kloosterman sums

  • Atish Dabholkar
  • João GomesEmail author
  • Sameer Murthy
Open Access
Regular Article - Theoretical Physics

Abstract

Non-perturbative quantum corrections to supersymmetric black hole entropy often involve nontrivial number-theoretic phases called Kloosterman sums. We show how these sums can be obtained naturally from the functional integral of supergravity in asymptotically AdS 2 space for a class of black holes. They are essentially topological in origin and correspond to charge-dependent phases arising from the various gauge and gravitational Chern-Simons terms and boundary Wilson lines evaluated on Dehn-filled solid 2-torus. These corrections are essential to obtain an integer from supergravity in agreement with the quantum degeneracies, and reveal an intriguing connection between topology, number theory, and quantum gravity. We give an assessment of the current understanding of quantum entropy of black holes.

Keywords

Black Holes in String Theory AdS-CFT Correspondence Supergravity Models Superstrings and Heterotic Strings 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHEParisFrance
  2. 2.CNRS, UMR 7589, LPTHEParisFrance
  3. 3.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeU.K.
  4. 4.Department of MathematicsKing’s CollegeLondonU.K.

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