An E11 invariant gauge fixing

TL;DR

This paper explores an E11 invariant gauge fixing in a non-linear realisation framework, deriving the tangent space metric and demonstrating gauge fixing methods that preserve E11 symmetry across multiple dimensions.

Contribution

It provides an alternative derivation of the invariant tangent space metric and shows how to gauge fix the non-linear realisation in an E11 invariant way.

Findings

Derived the invariant tangent space metric at low levels in multiple dimensions.

Demonstrated E11 invariant gauge fixing method.

Computed the tangent space metric explicitly in eleven, five, and four dimensions.

Abstract

We consider the non-linear realisation of the semi-direct product of E11 and its vector representation which leads to a spacetime with tangent group that is the Cartan involution invariant subalgera of E11. We give an alternative derivation of the invariant tangent space metric that this space-time possesses and compute this metric at low levels in eleven, five and four dimensions. We show that one can gauge fix the non-linear realisation in an E11 invariant manner.