Eisenstein Series and Instantons in String Theory

Abstract

In this thesis we review U-duality constraints on corrections to the type IIB supergravity effective action on torus compactifications. The U-duality invariant corrections are described by automorphic forms whose construction and Fourier expansion we explain. The latter enables us to extract physical information about instanton states in the theory. In particular, we discuss the first non-vanishing higher-derivative correction to the Einstein-Hilbert action in ten dimensions, for which there is a unique automorphic form incorporating all the perturbative and non-perturbative corrections in the string coupling constant.