Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes

Abstract

We present a holographic derivation of the entropy of supersymmetric asymptotically AdS${}_5$ black holes. We define a BPS limit of black hole thermodynamics by first focussing on a supersymmetric family of complexified solutions and then reaching extremality. We show that in this limit the black hole entropy is the Legendre transform of the on-shell gravitational action with respect to three chemical potentials subject to a constraint. This constraint follows from supersymmetry and regularity in the Euclidean bulk geometry. Further, we calculate, using localization, the exact partition function of the dual $\mathcal{N}=1$ SCFT on a twisted $S^1\times S^3$ with complexified chemical potentials obeying this constraint. This defines a generalization of the supersymmetric Casimir energy, whose Legendre transform at large $N$ exactly reproduces the Bekenstein-Hawking entropy of the black hole.

arXiv commentv4: minor changes, version published in JHEP

References in corpus (80)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• An Index for 4 dimensional Super Conformal Theories
• All supersymmetric solutions of minimal supergravity in five dimensions
• Rotation and the AdS/CFT correspondence
• Counting chiral primaries in N=1 d=4 superconformal field theories
• Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity
• Rigid Supersymmetric Theories in Curved Superspace
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• General supersymmetric AdS5 black holes
• General Non-Extremal Rotating Black Holes in Minimal Five-Dimensional Gauged Supergravity
• The Hagedorn Transition, Deconfinement and N=4 SYM Theory
• EXTREMAL BLACK HOLES AND ELEMENTARY STRING STATES
• Thermodynamics of Asymptotically Locally AdS Spacetimes
• Black hole microstates in AdS${}_4$ from supersymmetric localization
• Supersymmetric AdS5 black holes
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• The complete superconformal index for N=6 Chern-Simons theory
• A topologically twisted index for three-dimensional supersymmetric theories
• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• Sasaki-Einstein Manifolds and Volume Minimisation
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• Supersymmetric multi-charge AdS_5 black holes
• M5-branes from gauge theories on the 5-sphere
• Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions
• Supersymmetry on Curved Spaces and Holography
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Five-Dimensional Gauged Supergravity Black Holes with Independent Rotation Parameters
• Exploring Curved Superspace
• All supersymmetric solutions of minimal gauged supergravity in five dimensions
• 4d Index to 3d Index and 2d TQFT
• Localization on Hopf surfaces
• Exact microstate counting for dyonic black holes in AdS4
• An extremization principle for the entropy of rotating BPS black holes in AdS${}_5$
• Charged Kerr-de Sitter Black Holes in Five Dimensions
• Lectures on Quantum Black Holes
• The elliptic gamma function and SL(3,Z) x Z^3
• A Universal Counting of Black Hole Microstates in AdS${}_4$
• Quantum black holes, localization and the topological string
• Gauged supergravity from type IIB string theory on Y^{p,q} manifolds
• Entropy Function and AdS(2)/CFT(1) Correspondence
• Large $N$ matrix models for 3d $\mathcal{N}=2$ theories: twisted index, free energy and black holes
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• The $\mathcal{N}=1$ Chiral Multiplet on $T^2\times S^2$ and Supersymmetric Localization
• Entropy function and attractors for AdS black holes
• Rotating Hairy Black Holes
• Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS${}_5$ blackholes
• Supersymmetry in Lorentzian Curved Spaces and Holography
• Comments on 1/16 BPS Quantum States and Classical Configurations
• Supersymmetric Casimir Energy and the Anomaly Polynomial
• Mass of Rotating Black Holes in Gauged Supergravities
• A Note on Lie-Lorentz Derivatives
• Holographic renormalization and supersymmetry
• Large AdS black holes from QFT
• Supercurrent anomalies in 4d SCFTs
• Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions
• A note on the entropy of rotating BPS AdS${}_7\times S^4$ black holes
• 1/16-BPS Black Holes and Giant Gravitons in the AdS_5 X S^5 Space
• High-Temperature Expansion of Supersymmetric Partition Functions
• Comments on the Casimir energy in supersymmetric field theories
• Modular invariance on $S^1\times S^3$ and circle fibrations
• Entropy functional and the holographic attractor mechanism
• Thermodynamics at the BPS bound for Black Holes in AdS
• Evidence for the existence of a novel class of supersymmetric black holes with AdS${}_5\times$S${}^5$ asymptotics
• Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
• Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization
• Notes on non-extremal, charged, rotating black holes in minimal D=5 gauged supergravity
• Rotating Hairy Black Holes in AdS${}_5\times$S${}^5$
• The holographic supersymmetric Casimir energy
• Supergravitons from one loop perturbative N=4 SYM
• On the On-Shell: The Action of AdS${}_4$ Black Holes
• Comments on deconfinement in AdS/CFT
• The character of the supersymmetric Casimir energy
• Comments on supersymmetric solutions of minimal gauged supergravity in five dimensions
• Charges from Attractors
• Euclidean analysis of the entropy functional formalism
• A review on SUSY gauge theories on $S^3$
• Squashed, magnetized black holes in $D=5$ minimal gauged supergravity
• Near Horizon Analysis of Extremal AdS5 Black Holes
• Squashing the Boundary of Supersymmetric AdS${}_5$ Black Holes

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