Abstract
We present the supersymmetric extension of the recently constructed E8(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 E8(8). All bosonic fields are E8(8) tensors and transform under internal generalized diffeomorphisms. The fermions are tensors under the generalized Lorentz group SO(1, 2) × SO(16), where SO(16) is the maximal compact subgroup of E8(8). Vanishing generalized torsion determines the corresponding spin connections to the extent they are required to formulate the field equations and supersymmetry transformation laws. We determine the supersymmetry transformations for all bosonic and fermionic fields such that they consistently close into generalized diffeomorphisms. In particular, the covariantly constrained gauge vectors of E8(8) exceptional field theory combine with the standard supergravity fields into a single supermultiplet. We give the complete extended Lagrangian and show its invariance under supersymmetry. Upon solution of the section constraint the theory reduces to full D=11 or type IIB supergravity.
Highlights
Unique action functional — the exceptional field theory — which depending on the solution of the section constraint reproduces the full eleven-dimensional supergravity and full type IIB supergravity, respectively
We present the supersymmetric extension of the recently constructed E8(8) exceptional field theory — the manifestly U-duality covariant formulation of the untruncated ten- and eleven-dimensional supergravities
We determine the supersymmetry transformations for all bosonic and fermionic fields such that they consistently close into generalized diffeomorphisms
Summary
Since the section constraints (1.1) play a central role in the construction of the exceptional field theory, for the coupling of fermions it will be useful to spell out the decomposition of these constraints under the subgroup SO(16) according to (2.2). Which we will use in the following. The same algebraic constraints hold for derivatives ∂M replaced by the gauge connection Bμ M or its gauge parameter ΣM. Let us recall from [4] that these section constraints allow for (at least) two inequivalent solutions which break E8(8) to GL(8) or GL(7)×SL(2), and in which all fields depend on only eight or seven among the 248 internal coordinates Y M, respectively. The resulting theory coincides with the bosonic sector of D = 11 and type IIB supergravity, respectively
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