Microscopic Black Hole Entropy in Theories with Higher Derivatives

TL;DR

This paper develops a method to compute black hole entropy with higher derivative corrections in theories with AdS_3 geometries, aligning with Wald's formula and extending to nonextremal, nonsupersymmetric cases.

Contribution

It introduces a simple way to determine the spacetime central charge and entropy corrections using anomalies, applicable to a broad class of theories including string theory.

Findings

Reproduces corrected entropy formulas in string theory contexts.

Extends entropy calculations to nonextremal, nonsupersymmetric black holes.

Provides insight into exact results in four-dimensional theories ignoring R^4 corrections.

Abstract

We discuss higher derivative corrections to black hole entropy in theories that allow a near horizon AdS_3 x X geometry. In arbitrary theories with diffeomorphism invariance we show how to obtain the spacetime central charge in a simple way. Black hole entropy then follows from the Euclidean partition function, and we show that this gives agreement with Wald's formula. In string theory there are certain diffeomorphism anomalies that we exploit. We thereby reproduce some recent computations of corrected entropy formulas, and extend them to the nonextremal, nonsupersymetric context. Examples include black holes in M-theory on K3 x T^2, whose entropy reproduces that of the perturbative heterotic string with both right and left movers excited and angular momentum included. Our anomaly based approach also sheds light on why exact results have been obtained in four dimensions while ignoring R^4 type corrections.