Vertex Operators for the Supermembrane

TL;DR

This paper derives vertex operators for the supermembrane in 11 dimensions, showing their relation to superstring and superparticle operators, and discusses applications in matrix theory and supergravity backgrounds.

Contribution

It introduces vertex operators for the supermembrane that form a supersymmetry representation and connect to superstring and superparticle vertices, enabling new insights into supergravity couplings.

Findings

Vertex operators form a supersymmetry representation.

Reduce to superstring and superparticle vertices.

Enable derivation of matrix theory vertex operators.

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. We demonstrate that they form a representation of the supersymmetry algebra and reduce to the type IIA superstring vertex operators under double dimensional reduction, as well as to the vertices of the d=11 superparticle in the point-particle limit. As a byproduct, our results can be used to derive the corresponding vertex operators for matrix theory and to describe its linear coupling to an arbitrary d=11 supergravity background. Possible applications are discussed.