α′-Corrections to Extremal Dyonic Black Holes in Heterotic String Theory

We explicitly compute the entropy of an extremal dyonic black hole in heterotic string theory compactified on T 6 or K3 × 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 AdS3 near horizon geometry and space-time supersymmetry. For non-supersymmetric extremal black holes the result agrees with the one based on the assumption of AdS3 near horizon geometry and space-time supersymmetry of the underlying theory.