E11 in 11D

TL;DR

This paper constructs a non-linear realisation of E11 in eleven dimensions, deriving equations that match eleven-dimensional supergravity and extending previous results to include derivatives with respect to generalized coordinates.

Contribution

It provides a detailed construction of the E11 non-linear realisation in 11D, explicitly deriving supergravity equations from this framework, including new contributions involving generalized coordinates.

Findings

Equations of motion match 11D supergravity

Includes derivatives with respect to generalized coordinates

Extends previous E11 realisation results

Abstract

We construct the non-linear realisation of the semi-direct product of E11 and its vector representation in eleven dimensions and find the dynamical equations it predicts at low levels. These equations are completely determined by the non-linear realisation and when restricted to contain only the usual fields of supergravity and the usual space-time we find precisely the equations of motion of eleven dimensional supergravity. This paper extends the results announced in arXiv:1512.01644 and in particular it contains the contributions to the equations of motion that involve derivatives with respect to the level one generalised coordinates.