Duality Invariant Actions and Generalised Geometry

TL;DR

This paper develops a framework for duality-invariant actions using generalised geometry, constructing a non-linear realisation of E(11) and its representations to describe fields in various spacetime dimensions.

Contribution

It introduces a novel non-linear realisation approach for duality groups within generalised geometry, applicable to dimensions four to seven.

Findings

Constructed a non-linear realisation of E(11) and its fundamental representation.

Developed an invariant action on a generalised space with a generalised vielbein.

Focused on the duality group action within the generalised space.

Abstract

We construct the non-linear realisation of the semi-direct product of E(11) and its first fundamental representation at lowest order and appropriate to spacetime dimensions four to seven. This leads to a non-linear realisation of the duality groups and introduces fields that depend on a generalised space which possess a generalised vielbein. We focus on the part of the generalised space on which the duality groups alone act and construct an invariant action.