A configuration of 11-dimensional curved superspace as backgrounds for supermembrane

TL;DR

This paper constructs an 11-dimensional curved superspace configuration compatible with supermembrane theory, explicitly expressing supervielbein superfields in terms of supergravity component fields, ensuring κ-symmetry.

Contribution

It provides a detailed second-order supervielbein expansion in 11D superspace, linking supergravity components to supermembrane backgrounds using gauge completion.

Findings

Supervielbein superfields expressed up to second order in anticommuting coordinates.

Configuration maintains κ-symmetry for supermembrane Lagrangian.

Represents on-shell 11D supergravity in superspace form.

Abstract

We calculate all of vielbein superfields up to second order in anticommuting coordinates in terms of the component fields of 11-dimensional on-shell supergravity by using `Gauge completion'. This configuration of superspace holds the $\kappa $-symmetry for supermembrane Lagrangian and represents 11-dimensional on-shell supergravity.