Black Hole Entropy Associated with Supersymmetric Sigma Model

TL;DR

This paper derives the asymptotic spectrum degeneracy of a supersymmetric sigma model on symmetric products, linking it to black hole entropy corrections through elliptic genus partition functions.

Contribution

It introduces an identity connecting elliptic genus partition functions to second quantized string theory, enabling the derivation of asymptotic expansions relevant to black hole entropy.

Findings

Reproduces logarithmic corrections to black hole entropy

Derives asymptotic spectrum degeneracy for supersymmetric sigma models

Establishes a link between elliptic genus and string theory partition functions

Abstract

By means of an identity that equates elliptic genus partition function of a supersymmetric sigma model on the $N$-fold symmetric product $S^N X$ of $X$ ($S^N X=X^N/S_N$, $S_N$ 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.