Moonshine in Fivebrane Spacetimes

TL;DR

This paper explores BPS states in a specific string theory background, revealing a connection between mock modular forms, moonshine phenomena, and the elliptic genus of K3 surfaces.

Contribution

It provides a new expression for the helicity supertrace in terms of a mock modular form related to Mathieu moonshine.

Findings

Expressed the supertrace using the completion of a mock modular form

Established a link between moonshine and BPS state counting

Connected elliptic genus decomposition to Mathieu group M24

Abstract

We consider type II superstring theory on $K3 \times S^1 \times \mathbb{R}^{1,4}$ and study perturbative BPS states in the near-horizon background of two Neveu-Schwarz fivebranes whose world-volume wraps the $K3 \times S^1$ factor. These states are counted by the spacetime helicity supertrace $\chi_2(\tau)$ which we evaluate. We find a simple expression for $\chi_2(\tau)$ in terms of the completion of the mock modular form $H^{(2)}(\tau)$ that has appeared recently in studies of the decomposition of the elliptic genus of K3 surfaces into characters of the N=4 superconformal algebra and which manifests a moonshine connection to the Mathieu group $M_{24}$.