Asymptotic Expansion of the N=4 Dyon Degeneracy

Abstract

We study various aspects of power suppressed as well as exponentially suppressed corrections in the asymptotic expansion of the degeneracy of quarter BPS dyons in N=4 supersymmetric string theories. In particular we explicitly calculate the power suppressed corrections up to second order and the first exponentially suppressed corrections. We also propose a macroscopic origin of the exponentially suppressed corrections using the quantum entropy function formalism. This suggests a universal pattern of exponentially suppressed corrections to all four dimensional extremal black hole entropies in string theory.

LaTeX file, 2 figures, 28 pages; v2: added discussion on fermionic and bosonic zero modes of the AdS_2/Z_N solution, added references, rewrote footnote 4