On the quantum entropy function in 4d gauged supergravity

Abstract

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.