Nonlinear 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 E 11 proposal. June 20081 nicolas.boulanger@sns.it; Work supported by a "Progetto Italia" fellowship. 2 o.hohm@rug.nl

Exceptional field theory. III.E8(8)

“…As discussed in detail in the main text, the novel feature of this case is that the E 8p8q valued generalized metric M M N encodes components of the dual graviton but nevertheless allows for a consistent (in particular gauge invariant) dynamics thanks to the mechanism of constrained compensator fields introduced in [20] (that in turn is a duality-covariant extension of the proposal in [39]). This mechanism requires the presence of covariantly constrained gauge fields, which in the D " 3 case feature among the gauge vectors entering the covariant derivatives.…”

U-duality covariant gravity

“…However, it turns out that the techniques to deal with dual fields in gauged supergravity developed in [57,58] are quite sufficient to address this problem, a fact that has already been employed a while ago in [59,60], which will be crucial for our construction. This resolution of the 'dual graviton problem' (which can also be employed in a fully covariant framework [61][62][63]) may appear somewhat trivial, but as we will see is exactly what is needed in order to achieve a duality covariant formulation. While in this paper we will restrict ourselves to the 3 + n decomposition, we expect that along similar lines, using the techniques of gauged supergravity in generic dimensions, there will be formulations of the complete 11-dimensional supergravity that are covariant with respect to various U-duality groups.…”

The Dual Graviton in Duality Covariant Theories

“…Nevertheless, it is reasonable to ask whether there are reformulations of (super‐)gravity that feature a dual graviton‐type field and that are useful for particular applications. It is indeed possible (in a surprisingly trivial fashion) to formulate general relativity so that it contains the dual graviton together with the usual graviton and a compensator gauge field . This formulation is such that linearization about flat space yields, depending on a gauge choice, either standard linearized gravity or dual gravity, but this still begs the question what such a formulation is good for.…”

“…The vector fields generally contain the Kaluza‐Klein vectors , and so for the E 8(8) theory the question arises of how the eight components of should be interpreted, in particular how such a theory should be matched with supergravity, which does not contain a dual graviton. (One could introduce a dual graviton, using the formulation of [], but it should definitely be possible to match supergravity in the standard formulation. )…”

“…In the remainder of this review we explain this resolution of the dual graviton problem in more technical detail for different ExFTs and how it is useful for applications such as using generalized Scherk‐Schwarz compactifications for the consistency proofs of non‐toroidal Kaluza‐Klein truncations. Specifically, in Section 2 we review the dualization of linearized gravity and explain the compensator formulation of [] that describes full, non‐linear (super‐)gravity. Moreover, we discuss the dimensional reduction of the dual graviton, which sets the stage for our subsequent discussion of ExFT, where certain dimensionally reduced components of the dual graviton are visible.…”