The complete $D=11$ embedding of SO(8) supergravity

Abstract

The truncation formulae of $D=11$ supergravity on $S^7$ to $D=4$ $\mathcal{N}=8$ SO(8)-gauged supergravity are completed to include the full non-linear dependence of the $D=11$ three-form potential ${\hat{A}}_{(3)}$ on the $D=4$ fields, and their consistency is shown. The full embedding into ${\hat{A}}_{(3)}$ is naturally expressed in terms of a restricted version, still $\mathcal{N}=8$ but only SL(8)--covariant, of the $D=4$ tensor hierarchy. The redundancies introduced by this approach are removed at the level of the field strength ${\hat{F}}_{(4)}$ by exploiting $D=4$ duality relations. Finally, new expressions for the full consistent truncation formulae are given that are, for the first time, explicit in all $D=4$ fields.

10 pages

References in corpus (9)

• The maximal D=4 supergravities
• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• The string origin of dyonic $\mathcal{N}=8$ supergravity and its simple Chern-Simons duals
• Consistent Type IIB Reductions to Maximal 5D Supergravity
• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• Dyonic ISO(7) supergravity and the duality hierarchy
• Gauge Theories, Duality Relations and the Tensor Hierarchy
• Consistent $\mathcal{N}=8$ truncation of massive IIA on $S^6$
• IIB Supergravity and the E6(6) covariant vector-tensor hierarchy

Cited by in corpus (14)

• A master exceptional field theory
• AdS${}_4$ solutions of massive IIA from dyonic ISO(7) supergravity
• Brane-Jet Instabilities
• The Embedding of Gauged STU Supergravity in Eleven Dimensions
• Embedding the SU(3) sector of SO(8) supergravity in $D=11$
• A plethora of Type IIA embeddings for $d=5$ minimal supergravity
• Minimal $D=4$ $\mathcal{N}=2$ supergravity from $D=11$: An M-theory free lunch
• Universal properties of Kaluza-Klein gravitons
• Super-Chern-Simons spectra from Exceptional Field Theory
• Minimal $D=4$ truncations of type IIA
• Non-linear uplift Ansätze for the internal metric and the four-form field-strength of maximal supergravity
• Infinite and finite consistent truncations on deformed generalised parallelisations
• Consistent truncations from the geometry of sphere bundles
• Separability in Consistent Truncations