Vertex Operators for the Supermembrane and Background Field Matrix Theory

TL;DR

This paper derives vertex operators for the supermembrane in light cone gauge, enabling the coupling of matrix theory to supergravity backgrounds and analyzing scattering amplitudes consistent with supergravity predictions.

Contribution

It provides explicit vertex operators for the supermembrane, establishing a link between matrix theory and supergravity backgrounds to all orders.

Findings

Vertex operators derived for supermembrane emission processes.

Matrix theory coupled linearly to supergravity backgrounds.

3-point scattering amplitudes match supergravity results.

Abstract

We derive the vertex operators that are expected to govern the emission of the massless d=11 supermultiplet from the supermembrane in the light cone gauge. Our results immediately imply the linear coupling of matrix theory to an arbitrary supergravity background to all orders in anticommuting coordinates. Finally we address the definition of n-point tree level and one-loop scattering amplitudes. The resulting 3-point tree level amplitudes turn out to agree with d=11 supergravity and are completely fixed by supersymmetry and the existence of a normalizable ground state.