Heat Kernels on the AdS(2) cone and Logarithmic Corrections to Extremal Black Hole Entropy

Abstract

We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N=4 vector multiplet about a Z(N) orbifold of the near-horizon geometry of quarter--BPS black holes in N=4 supergravity. We find that this vanishes, matching perfectly with the prediction from the microstate counting. We also discuss possible generalisations of our heat kernel results to higher-spin fields over Z(N) orbifolds of higher-dimensional spheres and hyperboloids.

41 pages

References in corpus (14)

• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories
• Quantum W-symmetry in AdS_3
• Comments on the Spectrum of CHL Dyons
• Arithmetic of Quantum Entropy Function
• Product Representation of Dyon Partition Function in CHL Models
• A Farey tale for N=4 dyons
• Dyon Spectrum in N=4 Supersymmetric Type II String Theories
• Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
• Asymptotic Expansion of the N=4 Dyon Degeneracy
• Discrete Information from CHL Black Holes

Cited by in corpus (11)

• The 1/N correction in the D3-brane description of circular Wilson loop at strong coupling
• Logarithmic Corrections to $N\ge 2$ Black Hole Entropy
• Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets
• Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity
• Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function
• $Ad{S}_2$ holography is (non-)trivial for (non-)constant dilaton
• A Note on Vectorial AdS${}_5$/CFT${}_4$ Duality for Spin-$j$ Boundary Theory
• On Exponentially Suppressed Corrections to BMPV Black Hole Entropy
• Black hole one-loop determinants in the large dimension limit
• Central charges, elliptic genera, and Bekenstein-Hawking entropy in $\mathcal{N}=(2,2)$ AdS${}_3$/CFT${}_2$
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model