Supersymmetry, Localization and Quantum Entropy Function

Abstract

AdS_2/CFT_1 correspondence leads to a prescription for computing the degeneracy of black hole states in terms of path integral over string fields living on the near horizon geometry of the black hole. In this paper we make use of the enhanced supersymmetries of the near horizon geometry and localization techniques to argue that the path integral receives contribution only from a special class of string field configurations which are invariant under a subgroup of the supersymmetry transformations. We identify saddle points which are invariant under this subgroup. We also use our analysis to show that the integration over infinite number of zero modes generated by the asymptotic symmetries of AdS_2 generate a finite contribution to the path integral.

LaTeX file, 31 pages; v2: minor correction; v3: typos corrected

References in corpus (12)

• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• Comments on the Spectrum of CHL Dyons
• Entropy Function and AdS(2)/CFT(1) Correspondence
• Arithmetic of Quantum Entropy Function
• A Farey tale for N=4 dyons
• Ads(3)/CFT(2) to Ads(2)/CFT(1)
• Partition Functions of Torsion >1 Dyons in Heterotic String Theory on T^6
• Asymptotic Expansion of the N=4 Dyon Degeneracy
• Generalities of Quarter BPS Dyon Partition Function and Dyons of Torsion Two
• Duality Orbits, Dyon Spectrum and Gauge Theory Limit of Heterotic String Theory on T^6
• S-duality Action on Discrete T-duality Invariants

Cited by in corpus (28)

• Logarithmic Corrections to N=4 and N=8 Black Hole Entropy: A One Loop Test of Quantum Gravity
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Nonperturbative black hole entropy and Kloosterman sums
• Quantum black holes, localization and the topological string
• The Heat Kernel on AdS_3 and its Applications
• State Operator Correspondence and Entanglement in AdS_2/CFT_1
• All solutions of the localization equations for N=2 quantum black hole entropy
• Black Hole Microstate Counting and its Macroscopic Counterpart
• Finite Features of Quantum De Sitter Space
• Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets
• A Twist in the Dyon Partition Function
• BRST quantization and equivariant cohomology: localization with asymptotic boundaries
• Twisting and localization in supergravity: equivariant cohomology of BPS black holes
• Revisiting Leading Quantum Corrections to Near Extremal Black Hole Thermodynamics
• Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity
• Single-centered black hole microstate degeneracies from instantons in supergravity
• Negative discriminant states in N=4 supersymmetric string theories
• Topological AdS/CFT
• BPS State Counting in N=8 Supersymmetric String Theory for Pure D-brane Configurations
• Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function
• Heat Kernels on the AdS(2) cone and Logarithmic Corrections to Extremal Black Hole Entropy
• Functional determinants, index theorems, and exact quantum black hole entropy
• The gravitational path integral for $N=4$ BPS black holes from black hole microstate counting
• Gravitational free energy in topological AdS/CFT
• Quantum Black Hole Entropy, Localization and the Stringy Exclusion Principle
• Exact Half-BPS Black Hole Entropies in CHL Models from Rademacher Series
• On Exponentially Suppressed Corrections to BMPV Black Hole Entropy
• Supersymmetric localization: $\mathcal{N}=(2,2)$ theories on S${}^2$ and AdS${}_2$