On the quantum entropy function in 4d gauged supergravity

• Published in: The journal of high energy physics Vol. 2018; no. 7; pp. 1 - 45
• Main Authors: Hristov, Kiril, Lodato, Ivano, Reys, Valentin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2018; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Asymptotic properties; Black holes; Black Holes in String Theory; Classical and Quantum Gravitation; Elementary Particles; Entropy; Extended Supersymmetry; Field theory; Gauge-gravity correspondence; High energy physics; Integrals; M theory; Partitions (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Strings; Supergravity; Supersymmetry; Well construction; Black Holes in String Theory; AdS-CFT Correspondence; Gauge-gravity correspondence; Extended Supersymmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2018)072

A bstract 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 [1] in the AdS 2 ×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 AdS 4 ×S 7 Cacciatori-Klemm black holes [2] in M-theory and the asymptotically AdS 5 ×S 5 generalizations of Gutowski-Reall black holes [3] and Benini-Bobev black strings [4] in type IIB, as well as the recently constructed asymptotically AdS 4 ×S 6 solutions [5, 6] 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.