Partition function of dyonic black holes in N=4 string theory

TL;DR

This paper computes the dominant contribution to the partition function of dyonic black holes in N=4 string theory, compares it with topological string predictions, and explores duality covariance through perturbative corrections.

Contribution

It generalizes previous results to generic charges and refines the conjectured relation between black hole free energy and topological strings by including perturbative corrections.

Findings

Agreement with topological string predictions when perturbative corrections are included

Corrections modify the conjectured relation and ensure duality covariance

Provides a more complete understanding of black hole partition functions in N=4 string theory

Abstract

The dominant contribution to the semicanonical partition function of dyonic black holes of N=4 string theory is computed for generic charges, generalizing recent results of Shih and Yin. The result is compared to the black hole free energy obtained from the conjectured relation to topological strings. If certain perturbative corrections are included agreement is found to subleading order. These corrections modify the conjectured relation and implement covariance with respect to electric-magnetic duality transformations.