Superspace Geometry for Supermembrane Backgrounds

TL;DR

The paper advances the coupling of the 11D supermembrane to nontrivial supergravity backgrounds by constructing the superspace geometry, specifically the vielbein and tensor gauge field, in terms of on-shell component fields to second order in $\theta$. It provides explicit expressions and transformation rules up to $O(\theta^2)$, enabling κ-symmetric supermembrane actions in curved backgrounds and confirming supersymmetry covariance. The results lay groundwork for describing membrane dynamics and their curved-space matrix-theory analogues, and they yield leading surface terms for open membranes. Together, these developments open avenues for exploring membranes in AdS and flux backgrounds within the M-theory framework.

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.