On the positivity of black hole degeneracies in string theory

TL;DR

This paper proves that certain black hole degeneracy indices in string theory are positive integers, supporting their interpretation as exact quantum degeneracies, by leveraging the mock modular properties of their generating functions.

Contribution

It establishes the positivity of black hole degeneracy indices in specific string theory models using mock modular form properties, a novel mathematical approach.

Findings

Proves positivity of black hole degeneracy indices in certain string theories.

Uses mock modular properties to establish mathematical proof.

Supports the interpretation of indices as quantum degeneracies.

Abstract

Certain helicity trace indices of charged states in N=4 and N=8 superstring theory have been computed exactly using their explicit weakly coupled microscopic description. These indices are expected to count the exact quantum degeneracies of black holes carrying the same charges. In order for this interpretation to be consistent, these indices should be positive integers. We prove this positivity property for a class of four/five dimensional black holes in type II string theory compactified on T^6/T^5 and on K3 \times T^2/S^1. The proof relies on the mock modular properties of the corresponding generating functions.