Fermions and supersymmetry in \(E_{6(6)}\) exceptional field theory. (English) Zbl 1388.81155
Summary: We construct the supersymmetric completion of \(E_{6(6)}\)-covariant exceptional field theory. The theory is based on a (5 + 27)-dimensional generalized space-time subject to a covariant section constraint. The fermions are tensors under the local Lorentz group \(\mathrm{SO}(1, 4) \times USp(8)\) and transform as weighted scalars under the \(E_{6(6)}\) (internal) generalized diffeomorphisms. We present the complete Lagrangian and prove its invariance under supersymmetry. Upon explicit solution of the section constraint the theory embeds full \(D=1\)1 supergravity and IIB supergravity, respectively.
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