Linearized supergravity from Matrix theory

TL;DR

This work establishes that the linearized supergravity potential can be recovered from the one-loop Matrix theory potential to all orders in $1/r$ by identifying Matrix theory operators with the stress tensor and membrane currents. The leading and subleading terms, including higher moments, match the graviton and 3-form exchanges between arbitrary objects, with explicit checks for gravitons, membranes, and longitudinal 5-branes, and the authors extend the correspondence to an infinite series of higher-order terms in $F^4 X^n$. The analysis also reveals that finite-$N$ Matrix theory violates the equivalence principle, signaling that the finite-$N$ DLCQ description does not reduce to Einstein gravity and possibly reflects the underlying noncommutative geometry of Matrix theory. Overall, the paper strengthens the link between Matrix theory and linearized 11D supergravity while highlighting intrinsic limitations at finite $N$.

Abstract

We show that the linearized supergravity potential between two objects arising from the exchange of quanta with zero longitudinal momentum is reproduced to all orders in 1/r by terms in the one-loop Matrix theory potential. The essential ingredient in the proof is the identification of the Matrix theory quantities corresponding to moments of the stress tensor and membrane current. We also point out that finite-N Matrix theory violates the equivalence principle.