Angular momentum and long-range gravitational interactions in Matrix theory

TL;DR

This paper investigates the subleading long-range interactions in Matrix theory, demonstrating agreement with supergravity predictions for membrane-graviton potentials and extending the correspondence to all orders in the long-distance expansion.

Contribution

It provides a detailed analysis of subleading terms in the Matrix theory potential, establishing their precise match with supergravity calculations at all orders in the long-distance limit.

Findings

Subleading terms at order v/r^8 and v^3/r^8 are proportional to membrane angular momentum.

Matrix theory potential matches supergravity predictions for a graviton in a boosted Kerr metric.

The correspondence extends to all orders in the long-distance expansion, relating moments of stress-energy tensor to F^4 X^n terms.

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.