Understand
Understanding the implications of SL(2,Z) S-duality for the hypermultiplet moduli space of type II string theories has led to much progress recently in uncovering D-instanton contributions.
- In this work, we suggest that the extended duality group SL(3,Z), which includes both S-duality and Ehlers symmetry, may determine the contributions of D5 and NS5-branes.
- We support this claim by automorphizing the perturbative corrections to the "extended universal hypermultiplet", a five-dimensional universal SL(3,R)/SO(3) subspace which includes the string coupling, overall volume, Ramond zero-form and six-form and NS axion.
- Using the non-Abelian Fourier expansion of the Eisenstein series attached to the principal series of SL(3,R), first worked out by Vinogradov and Takhtajan 30 years ago, we extract the contributions of D(-1)-D5 and NS5-brane instantons, corresponding to the Abelian and non-Abelian coefficients, respectively.