Non-linear parent action and dual gravity

Abstract

We give a reformulation of non-linear Einstein gravity, which contains the dual graviton together with the ordinary metric and a shift gauge field. The metric does not enter through a `kinetic' Einstein-Hilbert term, but via topological couplings, and so the theory does not lead to a doubling of degrees of freedom. The field equations take the form of first-order duality relations. We analyze the gauge symmetries and comment on their meaning with regard to the E11 proposal.

15 pages, v2: version to appear in Phys.Rev.D, v3: typos corrected, footnote added after equations (3.31)-(3.32) with a reference to [7], v4: note added in introduction stating the equivalence of the field equations following from our action to those given previously by West in [7]

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Cited by in corpus (29)

• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• Exceptional Field Theory III: E${}_{8(8)}$
• Exceptional Field Theory II: E${}_{7(7)}$
• Supergravities without an Action: Gauging the Trombone
• Gauge Theories, Duality Relations and the Tensor Hierarchy
• Beyond E11
• A master exceptional field theory
• Off-Shell Hodge Dualities in Linearised Gravity and E11
• Manifest spin 2 duality with electric and magnetic sources
• Local E(11)
• On the E10/Massive Type IIA Supergravity Correspondence
• Twisted Self-Duality for Linearized Gravity in D dimensions
• Dual actions for massless, partially-massless and massive gravitons in (A)dS
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• Can dual gravity be reconciled with E11?
• Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4
• Frame-like off-shell dualisation for mixed-symmetry gauge fields
• Spin-2 twisted duality in (A)dS
• Dual gravity and E11
• Prepotentials for linearized supergravity
• Dual linearized gravity in D=6 coupled to a purely spin-two field of mixed symmetry (2,2)
• A note on "gaugings" in four spacetime dimensions and electric-magnetic duality
• Unfolding $E_{11}$
• Non-linear parent action and dual N=1 D=4 supergravity
• Electric-magnetic duality in linearized Hořava-Lifshitz gravity
• Aspects of electric-magnetic dualities in maximal supergravity
• String Dualities and Gaugings of Supergravity
• Dual Fields of Massive/Massless Gravitons in IR/UV Completions
• Yes-go cross-couplings in collections of tensor fields with mixed symmetries of the type (3,1) and (2,2)