E$_{8(8)}$ Exceptional Field Theory: Geometry, Fermions and Supersymmetry

Understand

We present the supersymmetric extension of the recently constructed E$_{8(8)}$ exceptional field theory -- the manifestly U-duality covariant formulation of the untruncated ten- and eleven-dimensional supergravities.

• This theory is formulated on a (3+248) dimensional spacetime (modulo section constraint) in which the extended coordinates transform in the adjoint representation of E$_{8(8)}$.
• All bosonic fields are E$_{8(8)}$ tensors and transform under internal generalized diffeomorphisms.
• The fermions are tensors under the generalized Lorentz group SO(1,2)$\times$SO(16), where SO(16) is the maximal compact subgroup of E$_{8(8)}$.