On membrane interaction in Matrix theory

Abstract

We compute the interaction potential between two parallel transversely boosted wrapped membranes (with fixed momentum p −) in D = 11 supergravity with compact light-like direction. We show that the supergravity result is in exact agreement with the potential following from the all-order Born-Infeld-type action conjectured to be the leading planar infra-red part of the quantum super Yang-Mills effective action. This provides a non-trivial test of consistency of the arguments relating Matrix theory to a special limit of type II string theory. We also find the potential between two (2+0) D-brane bound states in D = 10 supergravity (corresponding to the case of boosted membrane configuration in 11-dimensional theory compactified on a space-like direction). We demonstrate that the result reduces to the SYM expression for the potential in the special low-energy ( α′ → 0) limit, in agreement with previous suggestions. In an appendix we derive the action obtained from the D = 11 membrane action by the world-volume duality transformation of the light-like coordinate x − into a 3-vector.