Unfolding $E_{11}$

TL;DR

This paper develops an unfolded formulation for fields in the non-linear realization of $E_{11}$, proposing an infinite set of duality relations and exploring the origin of additional fields beyond $E_{11}$.

Contribution

It introduces a novel unfolded formalism for $E_{11}$ fields and proposes an infinite hierarchy of duality relations at the linearized level.

Findings

Derived the unfolded formulation of $E_{11}$ fields.

Proposed an infinite set of duality relations.

Explored the origin of extra fields outside $E_{11}$.

Abstract

We work out the unfolded formulation of the fields in the non-linear realisation of $E_{11}$. Using the connections in this formalism, we propose, at the linearised level, an infinite number of first-order duality relations between the dual fields in $E_{11}$. In this way, we introduce extra fields that do not belong to $E_{11}$ and we investigate their origin. The equations of motion of the fields are obtained by taking derivatives and higher traces of the duality relations.