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Title
Abstract
Localization Procedure
Main Result
Summary of the Localizing Manifold
Finite Result and Saddle-Point Evaluation
Conclusion and Discussion
References

On the quantum entropy function in 4d gauged supergravity

Profile image of Ivano LodatoIvano Lodato

Journal of High Energy Physics

https://doi.org/10.1007/JHEP07(2018)072
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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 finitedimensional 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.

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    seyed mohammadreza hosseini

    Journal of High Energy Physics, 2019

    The entropy of a class of asymptotically AdS4 magnetically charged BPS black holes can be obtained by extremizing the topologically twisted index of the dual three-dimensional field theory. This principle is known as $$ \mathcal{I} $$ I -extremization. A gravitational dual of $$ \mathcal{I} $$ I -extremization for a class of theories obtained by twisted compactifications of M2-branes living at a Calabi-Yau four-fold has been recently proposed. In this paper we investigate the relation between the two extremization principles. We show that the two extremization procedures are equivalent for theories without baryonic symmetries, which include ABJM and the theory dual to the non-toric Sasaki-Einstein manifold V 5,2. We then consider a class of quivers dual to M2-branes at toric Calabi-Yau four-folds for which the $$ \mathcal{I} $$ I -functional can be computed in the large N limit, and depends on three mesonic fluxes. We propose a gravitational dual for this construction, that we call ...

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