On the quantum entropy function in 4d gauged supergravity

Abstract

We analyze BPS black hole attractors in the conformal 4d gauged supergravity formalism and apply the technique known as supergravity localization in order to evaluate Sen's quantum entropy function in the ${\mathrm{AdS}}_2\times {\mathrm{S}}^2$ near-horizon geometry. Under certain assumptions, we reduce the exact expression of the functional integral to a finite-dimensional integral for a number of supersymmetric black holes in gauged supergravity with AdS asymptotics subject to a holographic description via a dual field theory. Examples include the asymptotically ${\mathrm{AdS}}_4\times {\mathrm{S}}^7$ Cacciatori-Klemm black holes in M-theory and the asymptotically ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ generalizations of Gutowski-Reall black holes and Benini-Bobev black strings in type IIB, as well as the recently constructed asymptotically ${\mathrm{AdS}}_4\times {\mathrm{S}}^6$ solutions in massive type IIA. Our results provide an important first step towards a gravitational counterpart to the exact evaluation of supersymmetric partition functions at finite $N$ for the holographically dual field theories in these examples.

arXiv comment49 pages; extended analysis of BPS equations and corrected typos in v2

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• Gluing gravitational blocks for AdS black holes
• Topologically twisted indices in five dimensions and holography
• Microscopic Entropy of Rotating Electrically Charged AdS${}_4$ Black Holes from Field Theory Localization
• Localization of the action in AdS/CFT
• Rotating attractors and BPS black holes in $Ad{S}_4$
• Universal 3d Cardy Block and Black Hole Entropy
• Rotating Black Hole Entropy from M5-branes
• Geometry of $\mathcal{I}$-extremization and black holes microstates
• 6D attractors and black hole microstates
• Large $N$ Partition Functions of the ABJM Theory
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• Black hole microstate counting in Type IIB from 5d SCFTs
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• ABJM at finite $N$ via 4d supergravity
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS${}_4$ Black Holes
• One-loop determinants for black holes in 4d gauged supergravity
• The Topologically Twisted Index in the 't Hooft Limit and the Dual AdS${}_4$ Black Hole Entropy
• Logarithmic correction to black hole entropy in universal low-energy string theory models
• Non-topological logarithmic corrections in minimal gauged supergravity
• Universal Entropy and Hawking Radiation of Near-Extremal AdS${}_4$ Black Holes
• On the off-shell formulation of N=2 supergravity with tensor multiplets
• Quantum entropy of BMPV black holes and the topological M-theory conjecture
• Rotating black holes in the FI-gauged $N=2$, $D=4$ ${\overline{\mathbb{C}\text{P}}}^n$ model
• Boundary Conditions in Topological AdS${}_4$/CFT${}_3$