A geometric formulation of exceptional field theory

TL;DR

This paper develops a coordinate-invariant formulation of the full bosonic SL(5) exceptional field theory, interpreting the extended space as a manifold with a specific structure, and constructs an action accommodating non-flat structures.

Contribution

It provides a geometric, coordinate-invariant formulation of the full bosonic SL(5) exceptional field theory, including an action for non-flat structures.

Findings

Algebra of generalized diffeomorphisms closes with specific constraints.

The formulation interprets the extended space as a manifold with SL(5)×R+ structure.

An action is constructed for the bosonic SL(5) exceptional field theory.

Abstract

We formulate the full bosonic SL(5) exceptional field theory in a coordinate-invariant manner. Thereby we interpret the 10-dimensional extended space as a manifold with $\mathrm{SL}(5)\times\mathbb{R}^+$-structure. We show that the algebra of generalised diffeomorphisms closes subject to a set of closure constraints which are reminiscent of the quadratic and linear constraints of maximal seven-dimensional gauged supergravities, as well as the section condition. We construct an action for the full bosonic SL(5) exceptional field theory, even when the $\mathrm{SL}(5)\times\mathbb{R}^+$-structure is not locally flat.