Abstract
We show how the gauge and field structure of the tensor hierarchies in Double and E7(7) Exceptional Field Theory fits into L∞ algebras. Special attention is paid to redefinitions, the role of covariantly constrained fields and intertwiners. The results are connected to Gauged Supergravities through generalized Scherk-Schwarz reductions. We find that certain gauging-dependent parameters generate trivial gauge transformations, giving rise to novel symmetries for symmetries that are absent in their ungauged counterparts.
Highlights
Paper by a number additional examples of field theories fitting into L∞ algebras: ChernSimons theories, Einstein gravity, etc
We show how the gauge and field structure of the tensor hierarchies in Double and E7(7) Exceptional Field Theory fits into L∞ algebras
We find that certain gauging-dependent parameters generate trivial gauge transformations, giving rise to novel symmetries for symmetries that are absent in their ungauged counterparts
Summary
We review the KK-formulation of DFT [39]. We present in the appendix the relation of this formulation with the generalized metric approach [53]. We will deal with two different sets of parameters, related by field-redefinitions Those noted with a hat (Λ , Ξ) are such that the gauge transformations can be written in a covariant form with respect to internal generalized diffeomorphisms. But only for the particular set of un-hatted parameters the brackets are field-independent ξ1μ2 = [ξ1 , ξ2]μ + ΛP[1∂P ξ2μ] , ΛM 12 = [Λ1 , Λ2]M (C) + 2ξ[ρ1∂ρΛM 2] + ξ[ρ1∂M Ξ2]ρ + Ξ[1ρ∂M ξ2ρ] , Ξ12 μ = 2ΛP[1∂P Ξ2]μ + ΛP[1∂μΛ2]P + ξ[ρ1∂ρΞ2]μ − ξ[ρ1∂μΞ2]ρ − Ξ[1ρ∂μξ2ρ] This fact makes this set of parameter convenient to explore how the DFT tensor hierarchy fits into an L∞ algebra.
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