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.

• Received 5 January 1998

DOI:https://doi.org/10.1103/PhysRevD.57.6464