Three-graviton scattering in Matrix theory revisited

TL;DR

This paper revisits three-graviton interactions in Matrix theory and supergravity, confirming certain terms vanish in Matrix theory and resolving previous discrepancies through lightlike compactification.

Contribution

It demonstrates the vanishing of specific three-graviton interaction terms in Matrix theory and reconciles this with supergravity via lightlike compactification.

Findings

Terms vanish in Matrix theory consistent with previous results.

Compatibility of supergravity and Matrix theory established through lightlike compactification.

Discussion on extending the analysis to arbitrary three-body systems.

Abstract

We consider a subset of the terms in the effective potential describing three-graviton interactions in Matrix theory and in classical eleven-dimensional supergravity. In agreement with the results of Dine and Rajaraman, we find that these terms vanish in Matrix theory. We show that the absence of these terms is compatible with the classical supergravity theory when the theory is compactified in a lightlike direction, resolving an apparent discrepancy between the two theories. A brief discussion is given of how this calculation might be generalized to compare the Matrix theory and supergravity descriptions of an arbitrary 3-body system.