E11, generalised space-time and IIA string theory

TL;DR

This paper constructs a systematic non-linear realisation of E11 and its fundamental representation in the context of IIA string theory, revealing underlying symmetries and connecting to doubled field theory.

Contribution

It provides a straightforward, systematic construction of a theory invariant under SO(10,10) x GL(1), incorporating gravity, two-form, and dilaton fields with extended coordinates.

Findings

The Lagrangian matches recent doubled field theory results.

The construction uncovers underlying symmetries of the theory.

It opens pathways to include R-R fields and higher-level coordinates.

Abstract

As advocated in hep-th/0307098 we construct the non-linear realisation of the semi-direct product of E11 and its first fundamental representation at lowest level from the IIA viewpoint. We find a theory that is SO(10,10)x GL(1) invariant and contains the fields of gravity, a two form and a dilaton but which depend on coordinates which belong to the vector representation of SO(10,10). The resulting Lagrangian agrees that of recent work on the so called doubled field theory. However, the construction given in this paper is straightforward and systematic. It also reveals the relevant underlying symmetries and opens the way to include the Ramond-Ramond, and higher level, fields together with additional coordinates of the generalised space-time.