Instantons, scale invariance and Lorentz invariance in matrix theory

In this paper we consider features of graviton scattering in Matrix theory compactified on a 2-torus. The features which interest us can only be determined by nonperturbative effects in the corresponding 2+1 dimensional super Yang Mills theory, We show that the superconformal symmetry of strongly coupled Super Yang Mills Theory in 2+1 dimensions almost determines low energy, large impact parameter ten dimensional graviton scattering at zero longitudinal momentum in the Matrix model of IIB string theory. We then show that amplitudes involving arbitrary transverse momentum transfer are governed by instanton processes similar to the Polchinski Pouliot process. Finally we consider the influence of instantons on a conjectured nonrenormalization theorem. This theorem is violated by instanton processes. Far from being a problem, this fact is seen to be crucial to the consistency of the IIB interpretation. We suggest that the SO(8) invariance of strongly coupled SYM theory may lead to a proof of eleven dimensional Lorentz invariance. (C) 1997 Published by Elsevier Science B.V.