Supersymmetry, Localization and Quantum Entropy Function

TL;DR

This paper applies localization techniques to the AdS_2/CFT_1 correspondence, identifying specific supersymmetric configurations that simplify the calculation of black hole entropy by reducing the path integral to key saddle points.

Contribution

It introduces a novel localization approach leveraging supersymmetry to evaluate the quantum entropy function for black holes in AdS_2 geometry.

Findings

Path integral localizes to supersymmetric invariant configurations.

Zero modes from asymptotic symmetries yield finite contributions.

Identification of saddle points invariant under supersymmetry subgroup.

Abstract

AdS_2/CFT_1 correspondence leads to a prescription for computing the degeneracy of black hole states in terms of path integral over string fields living on the near horizon geometry of the black hole. In this paper we make use of the enhanced supersymmetries of the near horizon geometry and localization techniques to argue that the path integral receives contribution only from a special class of string field configurations which are invariant under a subgroup of the supersymmetry transformations. We identify saddle points which are invariant under this subgroup. We also use our analysis to show that the integration over infinite number of zero modes generated by the asymptotic symmetries of AdS_2 generate a finite contribution to the path integral.