Angular momentum and long-range gravitational interactions in Matrix theory

Abstract

We consider subleading terms in the one-loop Matrix theory potential between a classical membrane state and a supergraviton. Nontrivial terms arise at order v/r^8 and v^3/r^8 which are proportional to the angular momentum of the membrane state. The effective potential for a graviton moving in a boosted Kerr-type metric is computed and shown to agree precisely with the Matrix theory calculation at leading order in the long-distance expansion for each power of the graviton velocity. This result generalizes to arbitrary order; we show that terms in the membrane-graviton potential corresponding to nth moments of the membrane stress-energy tensor are reproduced correctly to all orders in the long-distance expansion by terms of the form F^4 X^n in the one-loop Matrix theory calculation.