Can dual gravity be reconciled with E11?

TL;DR

This paper extends dual gravity formulations to eleven-dimensional supergravity, showing that E11 symmetry requires additional Stuckelberg fields and cannot be realized solely through gauge fixing.

Contribution

It introduces a supersymmetric action for dual gravity in eleven dimensions, incorporating Stuckelberg fields to realize E11 symmetries, highlighting the need for extended symmetry structures.

Findings

Dual gravity can be formulated with first-order duality relations.

E11 symmetry alone cannot be realized without Stuckelberg fields.

Additional symmetries are necessary for E11 to be a symmetry of supergravity.

Abstract

We extend a recently proposed formulation of dual gravity to the case of eleven-dimensional supergravity. The supersymmetric action corresponding to this alternative formulation is given, and it is shown that it leads to a set of first-order duality relations from which all second-order equations of motion follow as integrability conditions. On top of the fields corresponding to the conjectured E11 symmetry the action features Stuckelberg gauge fields that facilitate the realization of arbitrary symmetries on the dual graviton. However, there is no gauge-fixing that allows to eliminate the Stuckelberg fields. Therefore, E11 by itself is not a symmetry of eleven-dimensional supergravity but has to be extended at least by the Stuckelberg symmetries.