Membrane Scattering in Curved Space with M-Momentum Transfer

Abstract

We study membrane scattering in a curved space with non-zero M-momentum p_{11} transfer. In the low-energy short-distance region, the membrane dynamics is described by a three-dimensional N=4 supersymmetric gauge theory. We study an n-instanton process of the gauge theory, corresponding to the exchange of n units of p_{11}, and compare the result with the scattering amplitude computed in the low-energy long-distance region using supergravity. We find that they behave differently. We show that this result is not in contradiction with the large-N Matrix Theory conjecture, by pointing out that cutoff scales of the supergravity and the gauge theory are complementary to each other.