E11 and exceptional field theory

TL;DR

This paper shows that exceptional field theory can be derived as a truncation of the E11 non-linear realisation, revealing the connection between the two frameworks and suggesting the origin of the section condition.

Contribution

It demonstrates that exceptional field theory arises from a truncation of the E11 non-linear realisation, clarifying their relationship and the role of the section condition.

Findings

Exceptional field theory is a truncation of E11 non-linear realisation.

Higher level E11 symmetries are lost in the truncation.

The section condition may result from this truncation process.

Abstract

We demonstrate that exceptional field theory is a truncation of the non-linear realisation of the semi-direct product of E11 and its first fundamental as proposed in 2003. Evaluating the simple equations of the E11 approach, and using the commutators of the E11 algebra, we find the equations of exceptional field theory after making a radical truncation. This procedure does not respect any of the higher level E11 symmetries and so these are lost. We suggest that the need for the section condition in exceptional field theory could be a consequence of the truncation.