A geometric formulation of exceptional field theory

Understand

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.