Higher dualities in E11 exceptional field theory

TL;DR

This paper proves within E11 exceptional field theory at the linearised level that an infinite tower of higher dual fields can be incorporated, maintaining the same physical degrees of freedom as eleven-dimensional supergravity.

Contribution

It explicitly constructs parent actions for higher dual fields in E11 exceptional field theory, confirming the conjecture of an E11-invariant formulation of supergravity.

Findings

Higher dual fields propagate the same degrees of freedom as original fields.

Stueckelberg fields are shown to be pure curls, acting as sources for Labastida tensors.

The work confirms the conjecture at the linearised level within E11 exceptional field theory.

Abstract

It has been conjectured that there exists an E11-invariant formulation of eleven-dimensional supergravity in which the propagating fields of the theory are realised through an infinite tower of higher duals. In this work, we prove this conjecture explicitly within E11 exceptional field theory at the linearised level. Starting from the pseudo-Lagrangian, we construct parent actions for all higher gradient dual fields that are associated with the three-form, the six-form, and the dual graviton. We show that the resulting Euler-Lagrange equations constrain the Stueckelberg fields to be pure curls, ensuring that the higher duals propagate the same physical degrees of freedom as the original supergravity fields. The additional Stueckelberg fields, which are not predicted by the tensor hierarchy algebra, are shown to play a specific role as sources for the Labastida tensors of the higher dual fields.