Mathematics Colloquia and Seminars

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In this talk we will investigate the relationships between low energy four-particle scattering amplitudes of gauge particles and gravitons in the E8 × E8 and SO(32) heterotic string theories and the type I and type IA superstring theories by considering a variety of tree level and one loop Feynman diagrams describing such amplitudes in eleven-dimensional supergravity in a Horava–Witten background compactified on a circle. This accounts for a number of perturbative and non-perturbative aspects of low order higher derivative terms in the low energy expansion of string theory amplitudes, which are expected to be protected by half maximal supersymmetry from receiving corrections beyond one or two loops. We will also discuss the manner in which type I/heterotic duality may be realized for certain higher derivative interactions that are not so obviously protected. For example, our considerations suggest that t8t8R4 might receive no loop corrections beyond one loop. For this to be consistent with type I/heterotic duality, D-instanton contributions in the type I SO(32) theory and in the heterotic Spin(32)/Z2 theory appear to play an essential role.