On the quantum entropy function in 4d gauged supergravity

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) x 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) x S-7 Cacciatori-Klemm black holes [2] in M-theory and the asymptotically AdS(5) x S-5 generalizations of Gutowski-Reall black holes [3] and BeniniBobev black strings [4] in type IIB, as well as the recently constructed asymptotically AdS(4) xS(6) solutions [5, 6] in massive type HA. 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.