α′2-corrections to extremal dyonic black holes in heterotic string theory

We calculate α'2-corrections to the entropy of the 5-dimensional 3-charge and the 4-dimensional 4-charge large extremal black holes using the low energy effective action of the heterotic string theory. In the 4-dimensional case, our results are in agreement with the microscopic statistical entropy both for the BPS and the non-BPS black holes. In the more interesting 5-dimensional case, where the direct microscopic stringy description is still unknown, our results for the BPS black holes are in agreement with the results obtained from the action supplemented with R2-correction obtained by supersymmetric completion of the gravitational Chern-Simons term. This agreement does not extend to the non-BPS black holes, for which we propose a different expression for the entropy. We show that the new expression is supported by certain α'3-order calculations, and by the arguments based on the AdS/CFT correspondence.