Quantum Black Hole Entropy, Localization and the Stringy Exclusion Principle

Abstract

Supersymmetric localization has lead to remarkable progress in computing quantum corrections to BPS black hole entropy. The program has been successful especially for computing perturbative corrections to the Bekenstein-Hawking area formula. In this work, we consider non-perturbative corrections related to polar states in the Rademacher expansion, which describes the entropy in the microcanonical ensemble. We propose that these non-perturbative effects can be identified with a new family of saddles in the localization of the quantum entropy path integral. We argue that these saddles, which are euclidean $Ad{S}_2\times S^1\times S^2$ geometries, arise after turning on singular fluxes in M-theory on a Calabi-Yau. They cease to exist after a certain amount of flux, resulting in a finite number of geometries; the bound on that number is in precise agreement with the stringy exclusion principle. Localization of supergravity on these backgrounds gives rise to a finite tail of Bessel functions in agreement with the Rademacher expansion. As a check of our proposal, we test our results against well-known microscopic formulas for one-eighth and one-quarter BPS black holes in $\mathcal{N}=8$ and $\mathcal{N}=4$ string theory respectively, finding agreement. Our method breaks down precisely when mock-modular effects are expected in the entropy of one-quarter BPS dyons and we comment upon this. Furthermore, we mention possible applications of these results, including an exact formula for the entropy of four dimensional $\mathcal{N}=2$ black holes.

66 pages

References in corpus (21)

• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• A Farey Tail for Attractor Black Holes
• Nonperturbative black hole entropy and Kloosterman sums
• Supersymmetric Index from Black Hole Entropy
• Arithmetic of Quantum Entropy Function
• String Theory Effects on Five-Dimensional Black Hole Physics
• New supersymmetric higher-derivative couplings: Full N=2 superspace does not count!
• A Farey tale for N=4 dyons
• From AdS3/CFT2 to Black Holes/Topological Strings
• Ads(3)/CFT(2) to Ads(2)/CFT(1)
• Partition Functions of Torsion >1 Dyons in Heterotic String Theory on T^6
• The M5-Brane Elliptic Genus: Modularity and BPS States
• Logarithmic Corrections to $N\ge 2$ Black Hole Entropy
• Generating Charge from Diffeomorphisms
• U-duality Invariant Dyon Spectrum in type II on T^6
• Siegel Modular Forms and Black Hole Entropy
• Deformations of special geometry: in search of the topological string
• Mixed Rademacher and BPS Black Holes
• Generalized Kloosterman Sums from M2-branes

Cited by in corpus (5)

• Generalized Kloosterman Sums from M2-branes
• Exact Half-BPS Black Hole Entropies in CHL Models from Rademacher Series
• U-duality Invariant Quantum Entropy from Sums of Kloosterman Sums
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model
• On the exact entropy of $\mathcal{N}=2$ black holes