ON MEMBRANE INTERACTION IN MATRIX-THEORY

We compute the interaction potential between two parallel transversely boosted wrapped membranes (with fixed momentum p-) in D = 11 supergra vity 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 in fra-red part of the quantum super Yang-Mills effective action. This pr ovides a non-trivial test of consistency of the arguments relating Mat rix theory to a special limit of type II string theory. We also find t he potential between two (2 + 0) D-brane bound states in D = 10 superg ravity (corresponding to the case of boosted membrane configuration in 11-dimensional theory compactified on a space-like direction). We dem onstrate that the result reduces to the SYM expression for the potenti al in the special low-energy (alpha' --> 0) limit, in agreement with p revious 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. (C) 1998 Elsevier Science B.V.