Superspace Geometry for Supermembrane Backgrounds

TL;DR

This paper develops a superspace framework for supermembrane backgrounds, enabling the description of supermembranes in complex supergravity environments and verifying key invariances of the action.

Contribution

It constructs superspace vielbein and tensor gauge fields from 11D supergravity components, facilitating supermembrane analysis in nontrivial backgrounds to second order.

Findings

Superspace vielbein and gauge fields expressed in supergravity terms

Supermembrane action shown to be kappa-invariant at second order

Action maintains supersymmetry covariance and proper surface terms

Abstract

We construct part of the superspace vielbein and tensor gauge field in terms of the component fields of 11-dimensional on-shell supergravity. The result can be utilized to describe supermembranes and corresponding matrix models for Dirichlet particles in nontrivial supergravity backgrounds to second order in anticommuting coordinates. We exhibit the kappa-invariance of the corresponding supermembrane action, which at this order holds for unrestricted supergravity backgrounds, the supersymmetry covariance and the resulting surface terms in the action.