Three-graviton scattering and recoil effects in M-atrix theory

We study the scattering of three gravitons in M-atrix theory at finite N. With a specific choice of the background we obtain the complete result up to two loops. The contributions from three-body forces agree with the ones presented in recent papers. We extend the calculation and evaluate the two-body exchanges as well. Such terms, somewhat difficult to isolate and compute, had been neglected so far in the existing literature. We show that the result we have obtained from M-atrix theory precisely matches the result from one-particle reducible tree diagrams in eleven-dimensional supergravity. (C) 2000 Elsevier Science B.V. All rights reserved.