Exceptional field theory: SO(5,5)

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 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.