Combinatorial Identities and Quantum State Densities of Supersymmetric Sigma Models on N-Folds

TL;DR

This paper investigates the link between quantum state counts in conformal theories and Lie algebra dimensions by computing asymptotic expansions of elliptic genera and black hole entropies, revealing new prefactors and corrections.

Contribution

It introduces novel calculations of state densities and entropy corrections in supersymmetric sigma models, highlighting precise prefactors and logarithmic terms.

Findings

Correct prefactors in state density expansions

Logarithmic corrections to black hole entropy

Enhanced understanding of conformal theory and Lie algebra connections

Abstract

There is a remarkable connection between the number of quantum states of conformal theories and the sequence of dimensions of Lie algebras. In this paper, we explore this connection by computing the asymptotic expansion of the elliptic genus and the microscopic entropy of black holes associated with (supersymmetric) sigma models. The new features of these results are the appearance of correct prefactors in the state density expansion and in the coefficient of the logarithmic correction to the entropy.