Consistent Kaluza-Klein Truncations via Exceptional Field Theory

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.

38 pages, 1 figure, v2: refs. added, typos corrected, to appear in JHEP

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Cited by in corpus (23)

• Exceptional field theory: $SO(5,5)$
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• Half-maximal supersymmetry from exceptional field theory
• Double Field Theory on Group Manifolds
• Fermions and Supersymmetry in ${\mathrm{E}}_{6(6)}$ Exceptional Field Theory
• Stable non-supersymmetric Anti-de Sitter vacua of massive IIA supergravity
• Generalised diffeomorphisms for E${}_9$
• Supersymmetric AdS${}_7$ and AdS${}_6$ vacua and their consistent truncations with vector multiplets
• E${}_{8(8)}$ Exceptional Field Theory: Geometry, Fermions and Supersymmetry
• O(d+1,d+1) enhanced double field theory
• A supersymmetric reduction on the three-sphere
• Kaluza-Klein fermion mass matrices from Exceptional Field Theory and $\mathcal{N}=1$ spectra
• Ten-dimensional origin of Minkowski vacua in $\mathcal{N}=8$ supergravity
• Locally non-geometric fluxes and missing momenta in M-theory
• New gaugings and non-geometry
• One-Loop $\beta$ Function of the Double Sigma Model with Constant Background
• Geometric non-geometry
• Old and new vacua of 5D maximal supergravity
• Extended Drinfel'd algebras and non-Abelian duality
• Generalized Cartan Calculus in general dimension
• Wrapped NS5-Branes, Consistent Truncations and Inönü-Wigner Contractions
• The many facets of exceptional field theory
• Generalised U-dual solutions in supergravity