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.

23 pages + Appendix

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• Exceptional field theory: $SO(5,5)$
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• Half-maximal supersymmetry from exceptional field theory
• Exotic branes and non-geometric fluxes
• E${}_{8(8)}$ Exceptional Field Theory: Geometry, Fermions and Supersymmetry
• Polyvector deformations in eleven-dimensional supergravity
• Generalized 11D supergravity equations from tri-vector deformations
• Geometric non-geometry
• Polyvector deformations of Type IIB backgrounds
• Exceptional Field Theory for $E_{6(6)}$ supergravity
• SUSY and tri-vector deformations
• Duality Covariant Solutions in Extended Field Theories
• Exotic Aspects of Extended Field Theories
• The canonical formulation of E${}_{6(6)}$ exceptional field theory