Black hole entropy associated with the supersymmetric sigma model

Abstract

By means of an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the N-fold symmetric product [Formula Presented] of X [Formula Presented] where [Formula Presented] is the symmetric group of N elements) to the partition function of a second-quantized string theory, we derive the asymptotic expansion of the partition function as well as the asymptotic for the degeneracy of spectrum in string theory. The asymptotic expansion for the state counting reproduces the logarithmic correction to the black hole entropy. © 2003 The American Physical Society.