Superconformal Symmetry in 11D Superspace and the M-Theory Effective Action

TL;DR

This paper explores the role of superconformal symmetry in 11D superspace, proposing that such symmetry is relevant for the M-theory effective action and demonstrating how non-trivial torsion tensors relate to conformal compensators and M-theory corrections.

Contribution

It establishes a theorem linking 11D supergravity fluctuations to conformal geometry and presents a superspace realization of Weyl symmetry relevant for M-theory.

Findings

Non-vanishing dimension 1/2 torsion tensors are necessary for conformal compensators.

A minimal superspace realization of Weyl symmetry in 11D is constructed.

Conformal symmetry likely plays a role in the M-theory effective action.

Abstract

We establish a theorem about non-trivial 11D supergravity fluctuations that are conformally related to flat superspace geometry. Under the assumption that a theory of conformal 11D supergravity exists, similar in form to that of previously constructed theories in lower dimensions, this theorem demands the appearance of non-vanishing dimension 1/2 torsion tensors in order to accommodate a non-trivial 11D conformal compensator and thus M-theory corrections that break super-conformal symmetry. At the complete non-linear level, a presentation of a conventional minimal superspace realization of Weyl symmetry in eleven dimensional superspace is also described. All of our results taken together imply that there exists some realization of conformal symmetry relevant for the M-theory effective action. We thus led to conjecture this is also true for the full and complete M-theory.