Asymptotics of Elliptic Genera of Symmetric Products and Dyonic Black Hole Degeneracy

TL;DR

This paper derives asymptotic formulas for elliptic genera of symmetric product spaces and applies these results to estimate the degeneracy of dyonic black holes, linking geometry, quantum field theory, and black hole physics.

Contribution

It provides new asymptotic expansions for elliptic genera of symmetric products and connects these to black hole degeneracy calculations.

Findings

Asymptotic expansions for elliptic genera are obtained.

Degeneracy formulas for dyonic black holes are derived.

Results bridge geometric invariants and black hole microstates.

Abstract

We calculate asymptotic expansions of elliptic genera for a supersymmetric sigma model on the N - fold symmetric product S^NM of a Kahler manifold M and for N = 2 superconformal field theory. Asymptotic expansions for the degeneracy of dyonic black hole spectrum are also derived.