Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets

TL;DR

This paper applies supersymmetric localization to compute the exact one-loop partition function for vector multiplets in N=2 supergravity, providing insights into quantum corrections to BPS black hole entropy.

Contribution

It introduces a method to evaluate the one-loop determinant for vector multiplets using localization, including a proposed functional measure, in the context of BPS black hole entropy.

Findings

One-loop determinant expressed in terms of the physical metric radius.

Consistency with known logarithmic corrections to black hole entropy.

Explicit saddle point solutions for vector multiplets in AdS_2 x S^2 background.

Abstract

We use the techniques of supersymmetric localization to compute the BPS black hole entropy in N=2 supergravity. We focus on the n_v+1 vector multiplets on the black hole near horizon background which is AdS_2 x S^2 space. We find the localizing saddle point of the vector multiplets by solving the localization equations, and compute the exact one loop partition function on the saddle point. Furthermore, we propose the appropriate functional integration measure. Through this measure, the one loop determinant is written in terms of the radius of the physical metric, which depends on the localizing saddle point value of the vector multiplets. The result for the one loop determinant is consistent with the logarithmic corrections to the BPS black hole entropy from vector multiplets.