Graviton scattering amplitudes in M theory

Abstract

We compute graviton scattering amplitudes in M theory using Feynman rules for a scalar particle coupled to gravity in eleven dimensions. The processes that we consider describe the single graviton exchange and the double graviton exchange, that in M(atrix) theory correspond to the v^4/r^7 and v^6/r^14 term, respectively. We argue that the v^6/r^14 term appearing in M(atrix) theory at two loops can be obtained from the covariant eleven-dimensional four-graviton amplitude. Finally, we calculate the v^8/r^18 term appearing at two loops in M(atrix) theory. It has been previously conjectured that this term is related to a four graviton scattering amplitude involving the R^4 vertex of M theory.