Moonshine in fivebrane spacetimes

We consider type II superstring theory on K3×S¹×ℝ^1,4 and study perturbative BPS states in the near-horizon background of two Neveu-Schwarz fivebranes whose world-volume wraps the K3×S¹ factor. These states are counted by the spacetime helicity supertrace χ₂(τ) which we evaluate. We find a simple expression for χ₂(τ) in terms of the completion of the mock modular form H⁽²⁾(τ) 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 M₂₄