Angular momentum and long-range gravitational interactions in Matrix theory

TL;DR

This work analyzes subleading long-range interactions in Matrix theory, showing that stationary terms at orders $v/r^8$ and $v^3/r^8$ are governed by the membrane's angular momentum and, more generally, by higher moments of the membrane stress-energy tensor. By performing a one-loop calculation and comparing to a boosted Kerr-type supergravity background (as well as to single-graviton exchange in 11D supergravity), the authors demonstrate an exact correspondence between the Matrix theory potential and gravitational predictions at leading orders in the long-distance expansion for each velocity power, and they extend this correspondence to all orders via higher moments captured by $F^4 X^n$ terms. They provide explicit analyses, including a rotating spherical membrane example, that finite-$N$ effects can modify the simple angular-momentum–to–potential relation, offering insight into the limits of the equivalence principle in DLCQ settings. Overall, the paper strengthens the evidence that Matrix theory encodes detailed gravitational physics of 11D supergravity through structured, moment-based interactions.

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.