alpha'-Corrections to Extremal Dyonic Black Holes in Heterotic String Theory

TL;DR

The paper addresses the entropy of extremal dyonic black holes in heterotic string theory by incorporating all tree-level four-derivative corrections. It develops a covariant framework to handle the gravitational Chern-Simons term via a six-dimensional auxiliary 2-form and a dual scalar, enabling a consistent four-dimensional entropy-function calculation. The leading entropy ${\cal E}_0$ arises from 6D supergravity, while four-derivative corrections yield ${\cal E}_1'$, ${\cal E}_1''$; fixing the CS coefficient $\lambda=48$ produces a final entropy that matches earlier results and AdS$_3$ near-horizon arguments, supporting non-renormalization theorems in these settings. The work confirms that including the complete set of tree-level corrections aligns with prior SUSY-based and AdS$_3$-based predictions for both supersymmetric and non-supersymmetric cases, strengthening the robustness of the entropy computations in string theory.

Abstract

We explicitly compute the entropy of an extremal dyonic black hole in heterotic string theory compactified on T^6 or K3\times T^2 by taking into account all the tree level four derivative corrections to the low energy effective action. For supersymmetric black holes the result agrees with the answer obtained earlier 1) by including only the Gauss-Bonnet corrections to the effective action 2) by including all terms related to the curvature squared terms via space-time supersymmetry transformation, and 3) by using general arguments based on the assumption of AdS_3 near horizon geometry and space-time supersymmetry. For non-supersymmetric extremal black holes the result agrees with the one based on the assumption of AdS_3 near horizon geometry and space-time supersymmetry of the underlying theory.