Generalised geometry, eleven dimensions and E11

TL;DR

This paper constructs a non-linear realisation of E11 in eleven dimensions, incorporating extended coordinates, and demonstrates how it recovers known supergravity relations, suggesting an extension of maximal supergravity.

Contribution

It develops a new non-linear realisation of E11 with extended coordinates and explores its implications for supergravity and generalised geometry.

Findings

Recovered the self-duality relation for three and six form fields.

Extended the framework of maximal supergravity with additional coordinates.

Connected different approaches to generalised geometry.

Abstract

We construct the non-linear realisation of E11 and its first fundamental representation in eleven dimensions at low levels. The fields depend on the usual coordinates of space-time as well as two form and five form coordinates. We derive the terms in the dynamics that contain the three form and six form fields and show that when we restricted their field dependence to be only on the usual space-time we recover the correct self-duality relation. Should this result generalise to the gravity fields then the non-linear realisation is an extension of the maximal supergravity theory, as previously conjectured. We also comment on the connections between the different approaches to generalised geometry.