Logarithmic Correction to BPS Black Hole Entropy from Supersymmetric Index at Finite Temperature

TL;DR

This paper computes the logarithmic correction to BPS black hole entropy using a finite temperature supersymmetric index approach, confirming previous near horizon geometry results and testing the method's validity.

Contribution

It introduces an independent calculation of supersymmetric black hole entropy via a finite temperature index, validating previous zero-temperature results and extending the method's applicability.

Findings

Logarithmic correction matches previous near horizon geometry calculations.

Provides an independent verification of the supersymmetric index approach.

Tests the method on BPS black holes, confirming its consistency.

Abstract

It has been argued by Iliesiu, Kologlu and Turiaci in arXiv:2107.09062 that one can compute the supersymmetric index of black holes using black hole geometry carrying finite temperature but a specific complex angular velocity. We follow their prescription to compute the logarithmic correction to the entropy of BPS states in four dimensions, defined as the log of the index of supersymmetric black holes, and find perfect agreement with the previous results for the same quantity computed using the near horizon $AdS_2 \times S^2$ geometry of zero temperature black holes. Besides giving an independent computation of supersymmetric black hole entropy, this analysis also provides a test of the procedure used previously for computing logarithmic corrections to Schwarzschild and other non-extremal black hole entropy.