Supersymmetry and Membrane Interactions in M(atrix) Theory

TL;DR

This work investigates membrane–graviton interactions in BFSS Matrix theory, showing that boosting brane configurations along the eleventh dimension drives them toward approximate supersymmetry. By mapping boosted two-brane bound states to slowly moving 0-brane clusters via a chain of dualities, the authors demonstrate that the long-distance (supergravity) potentials agree with short-distance (Yang–Mills) potentials for these systems. They compute several one-loop potentials for graviton–membrane, membrane–anti-membrane, and moving/moving-brane configurations, consistently reproducing Type IIA results in the appropriate limits and validating the Matrix theory approach to M-theory in the infinite-momentum-frame regime. The results imply that Matrix theory can capture correct long-distance membrane dynamics and motivate further exploration of higher-brane bound states and compact-direction kinematics in this framework.

Abstract

We calculate the potential between various configurations of membranes and gravitons in M(atrix) theory. The computed potentials agree with the short distance potentials between corresponding 2-branes and 0-brane configurations in Type IIA string theory, bound to a large number of 0-branes to account for the boost to the infinite momentum frame. We show that, due to the large boost, these type IIA configurations are almost supersymmetric, so that the short and long distance potentials actually agree. Thus the M(atrix) theory is able to reproduce correct long distance behavior in these cases.