On membrane interaction in matrix theory

TL;DR

This paper verifies the consistency of Matrix theory with supergravity by computing membrane interaction potentials and matching them with super Yang-Mills predictions, providing evidence for the conjectured duality.

Contribution

It presents an exact supergravity calculation of membrane interactions that confirms the all-order Born-Infeld-type action's predictions, supporting Matrix theory's validity.

Findings

Supergravity potential matches the Born-Infeld-type action results.

Potential between D-brane bound states reduces to SYM expression at low energy.

Provides a non-trivial test of Matrix theory and string theory duality.

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 ($\a'\to 0$) limit, in agreement with previous suggestions. In 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.