Entropy Function for Heterotic Black Holes

TL;DR

This paper investigates how the Gauss-Bonnet term influences the entropy of extremal black holes in heterotic string theory, finding results identical to those with Weyl tensor squared terms, suggesting a simpler supergravity description.

Contribution

It demonstrates that the entropy and near horizon fields are unchanged when replacing Weyl tensor squared with Gauss-Bonnet terms, indicating a potential simplification in supergravity formulations.

Findings

Entropy results match those with Weyl tensor squared terms.

Attractor equations for axion-dilaton agree with supersymmetric theories.

Holomorphic anomaly effects on entropy are consistent with previous models.

Abstract

We use the entropy function formalism to study the effect of the Gauss-Bonnet term on the entropy of spherically symmetric extremal black holes in heterotic string theory in four dimensions. Surprisingly the resulting entropy and the near horizon metric, gauge field strengths and the axion-dilaton field are identical to those obtained by Cardoso et. al. for a supersymmetric version of the theory that contains Weyl tensor squared term instead of the Gauss-Bonnet term. We also study the effect of holomorphic anomaly on the entropy using our formalism. Again the resulting attractor equations for the axion-dilaton field and the black hole entropy agree with the corresponding equations for the supersymmetric version of the theory. These results suggest that there might be a simpler description of supergravity with curvature squared terms in which we supersymmetrize the Gauss-Bonnet term instead of the Weyl tensor squared term.