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 [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 Mtheory 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. arXiv:1803.05920v2 [hep-th]

One-loop determinants for black holes in 4d gauged supergravity

“…Here we review the set-up used in [1] to localize the path-integral (1.1) defined in [8] and describe the quantum entropy of black hole solutions in 4d N = 2 gauged supergravity with near-horizon geometry H 2 × S 2 . We choose coordinates 6) and turn on the relevant gauge and auxiliary fields in the Weyl multiplet to support half-BPS solutions, as well as a set of electric and magnetic charges and scalar fields in the vector multiplets fixed on-shell by the attractor mechanism of gauged supergravity.…”

“…A multitude of generalizations and related progress have since been reported (see [3] for an overview of the subject). In the present paper, which can be regarded as a sequel to [1], we aim to address systematically the problem of finding the quantum corrections to the Bekenstein-Hawking formula for the entropy of black holes. In the pursuit of finding an exact macroscopic entropy formula for black holes in gauged supergravity, we used the approach initiated in [4,5] for localization in supergravity.…”

“…In the pursuit of finding an exact macroscopic entropy formula for black holes in gauged supergravity, we used the approach initiated in [4,5] for localization in supergravity. The steps taken in [1] allowed us to determine the localization locus and classical action as will be reviewed shortly. The present work extends these steps to include the semi-classical analysis of one-loop determinants encoding the quadratic fluctuations around the localization locus.…”

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We continue the effort of defining and evaluating the quantum entropy function for supersymmetric black holes in 4d N = 2 gauged supergravity, initiated in [1]. The emphasis here is on the missing steps in the previous localization analysis, mainly dealing with one-loop determinants for abelian vector multiplets and hypermultiplets on the non-compact space H 2 × Σ g with particular boundary conditions.

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On the off-shell formulation of N = 2 supergravity with tensor multiplets

“…This, in turn, affects exact results that could be obtained on the computations of the black hole entropy by means of localization techniques [5][6][7], or on the stability properties of the selected vacuum when including non-perturbative effects. In fact, while there are natural corrections to the scalar potential that can be obtained from non-perturbative effects, it is more difficult to get similar results if the fundamental field in the theory is a tensor rather than a scalar.…”