Moonshine in Fivebrane Spacetimes

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 $M_{24}$.