Generalised geometry from the ground up

Abstract

Extending previous work on generalised geometry, we explicitly construct an E7-valued vielbein in eleven dimensions that encompasses the scalar bosonic degrees of freedom of D=11 supergravity, by identifying new "generalised vielbeine" in eleven dimensions associated with the dual 6-form potential and the dual graviton. By maintaining full on-shell equivalence with the original theory at every step, our construction altogether avoids the constraints usually encountered in other approaches to generalised geometry and, as a side product, also furnishes the non-linear ansatz for the dual (magnetic) 7-form flux for any non-trivial compactification of D=11 supergravity, complementing the known non-linear ansaetze for the metric and the 4-form flux. A preliminary analysis of the generalised vielbein postulate for the new vielbein components reveals tantalising hints of new structures beyond D=11 supergravity and ordinary space-time covariance, and also points to the possible D=11 origins of the embedding tensor. We discuss the extension of these results to E8.

20 pages + appendices

References in corpus (9)

• Double Field Theory
• Generalised Geometry for M-Theory
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• U-duality covariant gravity
• On the moduli space of spontaneously broken N = 8 supergravity
• Local E(11)
• Dual Gravity and Matter

Cited by in corpus (31)

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• Consistent $\mathcal{N}=8$ truncation of massive IIA on $S^6$
• IIB Supergravity and the E6(6) covariant vector-tensor hierarchy
• A master exceptional field theory
• Evidence for the existence of a novel class of supersymmetric black holes with AdS${}_5\times$S${}^5$ asymptotics
• On supersymmetric E11 exceptional field theory
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• The complete $D=11$ embedding of SO(8) supergravity
• Rotating Hairy Black Holes in AdS${}_5\times$S${}^5$
• Seeking the balance: Patching double and exceptional field theories
• $\mathcal{N}=2$ Supersymmetric Janus Solutions and Flows: From Gauged Supergravity to M Theory
• Uplifting non-compact gauged supergravities
• An SO(3)$\times$SO(3) invariant solution of $D=11$ supergravity
• E${}_{7(7)}$ Exceptional Field Theory in Superspace
• The Embedding of Gauged STU Supergravity in Eleven Dimensions
• Einstein-Cartan Calculus for Exceptional Geometry
• 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
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• Exceptional versus superPoincaré algebra as the defining symmetry of maximal supergravity
• Non-linear uplift Ansätze for the internal metric and the four-form field-strength of maximal supergravity
• About the (in)equivalence between holonomic versus non-holonomic theories of gravity
• Consistent truncations from the geometry of sphere bundles
• Dualized Gravity beyond Linear Approximation