On Graviton Scattering Amplitudes in M-Theory

TL;DR

This paper computes graviton scattering amplitudes in M-theory, connecting covariant eleven-dimensional results with M(atrix) theory predictions, and explores higher-order velocity and distance terms at two loops.

Contribution

It provides explicit calculations of graviton scattering amplitudes in M-theory and relates these to M(atrix) theory predictions, including higher-order terms.

Findings

Derived the $v^4/r^7$ and $v^6/r^{14}$ terms from scattering amplitudes.

Connected two-loop $v^6/r^{14}$ term to four-graviton amplitude with $R^4$-vertex.

Calculated the $v^8/r^{18}$ term at two loops, supporting conjectures about four-graviton scattering.

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 further show 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.