Entropy Function for Heterotic Black Holes

TL;DR

This paper uses the entropy function formalism to study how Gauss-Bonnet curvature corrections and holomorphic anomaly influence the entropy of extremal heterotic black holes in four dimensions. It shows that the resulting entropy and near-horizon data agree with results from supersymmetric theories that employ Weyl-tensor-squared corrections, suggesting a potential simpler supersymmetric completion based on Gauss-Bonnet terms. In the N=4 sector, the analysis yields S-duality covariant expressions for the corrected entropy and attractor equations that reproduce conjectured forms, even when holomorphicity is not straightforward. Overall, the work points to a unified, potentially simpler framework for curvature-squared corrections in supergravity and motivates further study of Gauss-Bonnet-based completions.

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.