Exceptional field theory: $SO(5,5)$

TL;DR

This paper develops an Exceptional Field Theory for the $SO(5,5)$ U-duality group, providing a unified geometric framework that encompasses maximal supergravities in various dimensions through extended spacetime and duality symmetries.

Contribution

It constructs a new $SO(5,5)$ exceptional field theory with a true action and duality-invariant pseudo-action, integrating the full extended spacetime and tensor hierarchy.

Findings

Formulation of $SO(5,5)$ exceptional field theory with a true action.

Demonstration of duality-invariant pseudo-action formulation.

Recovery of maximal supergravities in 11D and 10D from the theory.

Abstract

We construct Exceptional Field Theory for the group $SO(5,5)$ based on the extended (6+16)-dimensional spacetime, which after reduction gives the maximal $D=6$ supergravity. We present both a true action and a duality-invariant pseudo-action formulations. All the fields of the theory depend on the complete extended spacetime. The U-duality group $SO(5,5)$ is made a geometric symmetry of the theory by virtue of introducing the generalised Lie derivative that incorporates a local duality transformation. Tensor hierarchy appears as a natural consequence of the algebra of generalised Lie derivatives that are viewed as gauge transformations. Upon truncating different subsets of the extra coordinates, maximal supergravities in $D=11$ and $D=10$ (type IIB) can be recovered from this theory.