Nonperturbative black hole entropy and Kloosterman sums

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.

35 pages; minor changes, JHEP version

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Cited by in corpus (14)

• Universal low temperature theory of charged black holes with AdS${}_2$ horizons
• Exponential corrections to black hole entropy
• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
• Logarithmic Corrections to Entropy of Magnetically Charged AdS4 Black Holes
• A 2d/1d Holographic Duality
• Non-Pertubative Quantum Corrections to a Born-Infeld Black Hole and its Information Geometry
• Non-perturbative correction to the Horava-Lifshitz black hole thermodynamics
• The growth of the $\frac{1}{16}$-BPS index in 4d $\mathcal{N}=4$ SYM
• Phase transitions for deformations of JT supergravity and matrix models
• Chaotic Information Processing by Extremal Black Holes
• Generalized Kloosterman Sums from M2-branes
• Ramanujan and Quantum Black Holes
• U-duality Invariant Quantum Entropy from Sums of Kloosterman Sums
• On the exact entropy of $\mathcal{N}=2$ black holes