INSTANTONS, SCALE-INVARIANCE AND LORENTZ INVARIANCE IN MATRIX-THEORY

In this paper we consider features of graviton scattering in Matrix th eory compactified on a 2-torus. The features which interest us can onl y be determined by nonperturbative effects in the corresponding 2+1 di mensional super Yang Mills theory, We show that the superconformal sym metry of strongly coupled Super Yang Mills Theory in 2+1 dimensions al most determines low energy, large impact parameter ten dimensional gra viton scattering at zero longitudinal momentum in the Matrix model of IIB string theory. We then show that amplitudes involving arbitrary tr ansverse 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 theore m is violated by instanton processes. Far from being a problem, this f act 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.