Non-linear Kaluza-Klein theory for dual fields

Abstract

We present non-linear uplift ansaetze for all the bosonic degrees of freedom and dual fields in the 7-sphere reduction of D=11 supergravity to maximal SO(8) gauged supergravity and test them for the SO$(7{)}^{\pm }$ invariant solutions. In particular, we complete the known ansaetze for the internal components of the metric and 4-form flux by constructing a non-linear ansatz for the internal components of the dual 7-form flux. Furthermore, we provide ansaetze for the complete set of 56 vector fields, which are given by more general structures than those available from standard Kaluza-Klein theory. The novel features encountered here have no conventional geometric interpretation and provide a new perspective on Kaluza-Klein theory. We study the recently found set of generalised vielbein postulates and, for the 7-sphere compactification, we show that they reduce to the E7(7) Cartan equation of maximal SO(8) gauged supergravity in four dimensions. The significance of this framework for a higher-dimensional understanding of the embedding tensor and other gauged maximal supergravities is briefly discussed.

26 pages

References in corpus (4)

• Exceptional Form of D=11 Supergravity
• The maximal D=4 supergravities
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• Flux Compactifications of M-Theory on Twisted Tori

Cited by in corpus (24)

• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• Consistent Type IIB Reductions to Maximal 5D Supergravity
• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• Half-maximal supersymmetry from exceptional field theory
• Electric/magnetic duality and RG flows in AdS4/CFT3
• Consistent Pauli reduction on group manifolds
• IIB Supergravity and the E6(6) covariant vector-tensor hierarchy
• Evidence for the existence of a novel class of supersymmetric black holes with AdS${}_5\times$S${}^5$ asymptotics
• 7-dimensional $\mathcal{N}=2$ Consistent Truncations using $\mathrm{SL}(5)$ Exceptional Field Theory
• The complete $D=11$ embedding of SO(8) supergravity
• Rotating Hairy Black Holes in AdS${}_5\times$S${}^5$
• The embedding tensor of Scherk-Schwarz flux compactifications from eleven dimensions
• An SO(3)$\times$SO(3) invariant solution of $D=11$ supergravity
• The Embedding of Gauged STU Supergravity in Eleven Dimensions
• Flowing to Higher Dimensions: A New Strongly-Coupled Phase on M2 Branes
• Embedding the SU(3) sector of SO(8) supergravity in $D=11$
• Holographic dual of hot Polchinski-Strassler quark-gluon plasma
• Lobotomy of Flux Compactifications
• Gaugings from E7 Extended Geometries
• New gaugings and non-geometry
• On symmetries and dynamics of exotic supermultiplets
• Non-linear uplift Ansätze for the internal metric and the four-form field-strength of maximal supergravity
• Consistent 4-form fluxes for maximal supergravity