Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity

Abstract

We compute the logarithmic correction to black hole entropy about exponentially suppressed saddle points of the Quantum Entropy Function corresponding to Z(N) orbifolds of the near horizon geometry of the extremal black hole under study. By carefully accounting for zero mode contributions we show that the logarithmic contributions for quarter--BPS black holes in N=4 supergravity and one--eighth BPS black holes in N=8 supergravity perfectly match with the prediction from the microstate counting. We also find that the logarithmic contribution for half--BPS black holes in N = 2 supergravity depends non-trivially on the Z(N) orbifold. Our analysis draws heavily on the results we had previously obtained for heat kernel coefficients on Z(N) orbifolds of spheres and hyperboloids in arXiv:1311.6286 and we also propose a generalization of the Plancherel formula to Z(N) orbifolds of hyperboloids to an expression involving the Harish-Chandra character of SL(2,R), a result which is of possible mathematical interest.

40 pages

References in corpus (15)

• Near-horizon symmetries of extremal black holes
• 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
• Entropy Function and AdS(2)/CFT(1) Correspondence
• 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
• Dyon Spectrum in Generic N=4 Supersymmetric Z_N Orbifolds
• N=8 Dyon Partition Function and Walls of Marginal Stability
• Asymptotic Expansion of the N=4 Dyon Degeneracy
• Discrete Information from CHL Black Holes
• Heat Kernels on the AdS(2) cone and Logarithmic Corrections to Extremal Black Hole Entropy

Cited by in corpus (16)

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• Quantum Corrections to Supergravity on AdS${}_2\times S^2$
• Logarithmic Corrections to Black Hole Entropy: the Non-BPS Branch
• Logarithmic correction to black hole entropy in universal low-energy string theory models
• Siegel Modular Forms and Black Hole Entropy
• Seeley-DeWitt Coefficients in $\mathcal{N}=2$ Einstein-Maxwell Supergravity Theory and Logarithmic Corrections to $\mathcal{N}=2$ Extremal Black Hole Entropy
• Generalized Einstein-Maxwell theory: Seeley-DeWitt coefficients and logarithmic corrections to the entropy of extremal and non-extremal black holes
• Logarithmic corrections to black hole entropy in matter coupled $\mathcal{N}\ge 1$ Einstein-Maxwell supergravity
• A Note on Vectorial AdS${}_5$/CFT${}_4$ Duality for Spin-$j$ Boundary Theory
• Logarithmic correction to the entropy of a Kerr-Newman family of black holes in $U(1{)}^2$-charged STU supergravity models
• On Exponentially Suppressed Corrections to BMPV Black Hole Entropy
• Black hole one-loop determinants in the large dimension limit
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model