E11, Romans theory and higher level duality relations

TL;DR

This paper derives the complete linearised equations of motion for eleven-dimensional supergravity fields from E11 symmetry, revealing connections to Romans theory and introducing new duality relations.

Contribution

It provides the first comprehensive E11 invariant equations up to level four, including duality relations and their implications for supergravity and Romans theory.

Findings

Derived E11 invariant equations of motion up to level four.

Linked duality equations to second order supergravity equations.

Identified level four fields as origins of Romans theory.

Abstract

From the underlying non-linear realisation we compute the complete E11 invariant equations of motion in eleven dimensions, at the linearised level, up to and including level four in the fields. Thus we include the metric, the three and six forms, the dual graviton and three fields at level four. The fields are linked by a set of duality equations, which are first order in derivatives and transform into each other under the E11 symmetries. From these duality relations we deduce second order equations of motion, including those for the usual supergravity fields. As a result the on-shell degrees of freedom are those of the eleven dimensional supergravity. We also show that the level four fields provide an eleven dimensional origin of Romans theory and lead to a novel duality relation.