Fermions and Supersymmetry in ${\mathrm{E}}_{6(6)}$ Exceptional Field Theory

Abstract

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 $\mathrm{SO}(1,4)\times \mathrm{USp}(8)$ 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 $D=11$ supergravity and IIB supergravity, respectively.

arXiv comment23 pages + Appendix

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