Toward an Off - Shell 11D Supergravity Limit of M - Theory

TL;DR

This paper proposes a partial off-shell extension of 11D supergravity by introducing a spinor superfield, which could be relevant for M-theory and allows for auxiliary fields beyond the on-shell formulation.

Contribution

It introduces a new spinor superfield into 11D supergravity, enabling a partial off-shell formulation compatible with superspace Bianchi identities.

Findings

Identification of auxiliary fields via the superfield $J_\alpha$

Confirmation of $\kappa$-symmetry in the modified background

Potential relevance for systematic off-shell M-theory formulations

Abstract

We demonstrate that in addition to the usual fourth-rank superfield $(W_{a b c d})$ which describes the on-shell theory, a spinor superfield $(J_\a )$ can be introduced into the 11D geometrical tensors with engineering dimensions less or equal to one in such a way to satisfy the Bianchi identities in superspace. The components arising from $J_\a$ are identified as some of the auxiliary fields required for a full off-shell formulation. Our result indicates that eleven dimensional supergravity does not have to be completely on-shell. The $\k\-$symmetry of the supermembrane action in the presence of our partial off-shell supergravity background is also confirmed. Our modifications to eleven-dimensional supergravity theory are thus likely relevant for M-theory. We suggest our proposal as a significant systematic off-shell generalization of eleven-dimensional supergravity theory.