In this note we study the U-duality invariant coefficient functions of higher curvature corrections to the four-graviton scattering amplitude in type IIB string theory compactified on a torus. The main focus is on the D 6 R 4 term that is known to satisfy an inhomogeneous Laplace equation. We exhibit a novel method for solving this equation in terms of a Poincaré series ansatz and recover known results in D = 10 dimensions and find new results in D < 10 dimensions. We also apply the method to modular graph functions as they arise from closed superstring one-loop amplitudes.

Abstract. We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of SLn(A) are completely determined by certain highly degenerate Whittaker coefficients. We give an explicit formula for the Fourier expansion, analogously to the Piatetski-Shapiro-Shalika formula. In addition, we derive expressions for Fourier coefficients associated to all maximal parabolic subgroups. These results have potential applications for scattering amplitudes in string theory.

These proceedings from the second Caesar Lattes meeting in Rio de Janeiro 2015 are a brief introduction to how automorphic forms appear in the low energy effective action of maximally supersymmetric string theory. The explicit example of the R 4-interaction of type IIB string theory in ten dimensions is discussed. Its Fourier expansion is interpreted in terms of perturbative and non-perturbative contributions to the four graviton amplitude. HIGHER DERIVATIVE CORRECTIONS TO GENERAL RELATIVITY String theory offers an ultraviolet completion to general relativity. A good way of thinking about this is from the perspective of the low energy effective action. 1 A vector field, for example, with a vev would single out a distinguished direction in spacetime which would depend on the observer. 2 The vev of the axion plays a role analogous to that of the θ-angle in Yang-Mills theory.