The automorphic NS5-brane

Understanding the implications of SL(2,Z) S-duality on the hypermultiplet moduli space of type II string theories has led to much progress recently in uncovering D-instanton contributions. In this note, we suggest that the extended duality group SL(3,Z), which includes both S-duality and Ehlers symmetry, potentially determines the contributions of NS5-branes. We support this claim by automorphizing the perturbative corrections to the “extended universal hypermultiplet”, a five-dimensional universal SO(3)\SL(3) subspace which includes the string coupling, overall volume, Ramond zero-form and six-form and NS axion. In particular, we show that NS5-brane contributions are encoded by non-Abelian Fourier coefficients and satisfy a wave function property. We also conjecture that for models with a symmetric moduli space, the partition function of any number of NS5-branes is given by the minimal theta series of the corresponding duality group.