Abstract
We present the generalized Scherk-Schwarz reduction ansatz for the full supersymmetric exceptional field theory in terms of group valued twist matrices subject to consistency equations. With this ansatz the field equations precisely reduce to those of lower-dimensional gauged supergravity parametrized by an embedding tensor. We explicitly construct a family of twist matrices as solutions of the consistency equations. They induce gauged supergravities with gauge groups SO(p,q) and CSO(p,q,r). Geometrically, they describe compactifications on internal spaces given by spheres and (warped) hyperboloides $H^{p,q}$, thus extending the applicability of generalized Scherk-Schwarz reductions beyond homogeneous spaces. Together with the dictionary that relates exceptional field theory to D=11 and IIB supergravity, respectively, the construction defines an entire new family of consistent truncations of the original theories. These include not only compactifications on spheres of different dimensions (such as AdS$_5\times S^5$), but also various hyperboloid compactifications giving rise to a higher-dimensional embedding of supergravities with non-compact and non-semisimple gauge groups.
Highlights
From the fact that all retained massless fields are singlets under the resulting U(1)n gauge group
We describe the generalized Scherk-Schwarz ansatz for the full field content of the theory. We show that it defines a consistent truncation of the exceptional field theory (EFT) which reduces to the complete set of field equations of lower-dimensional gauged supergravity with embedding tensor ΘM α, θM, even in presence of a trombone gauging θM = 0
In this paper we have shown how the consistency of a large class of Kaluza-Klein truncations can be proved using exceptional field theory
Summary
The bosonic field content of the E7(7)-covariant exceptional field theory is given by eμα , MMN , AμM , Bμν α , Bμν M. The weights of the various bosonic fields of the theory are given by eμα MMN AμM Bμν α Bμν M λ: The generalized diffeomorphisms give rise to the definition of covariant derivatives (2.5). The full bosonic theory is invariant under vector and tensor gauge symmetries with parameters ΛM , Ξμ α, Ξμ M (the latter constrained according to (2.3)), as well as under generalized diffeomorphisms in the external coordinates Together, these symmetries uniquely fix all field equations. We close the discussion of the geometry by giving a definition of the generalized scalar curvature R that enters the potential It can be defined through a particular combination of second-order terms in covariant derivatives acting on an SO(1, 3) spinor in. The projections or contractions of covariant derivatives in these supersymmetry variations are again such that the undetermined connections drop out
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