Abstract
We present an implementation of a duality symmetry in the minimal linearized Hořava–Lifshitz gravity. Some difficulties arise when an attempt is made to implement off shell duality symmetries in theories that are not invariant under full spacetime diffeomorphisms. To avoid some of them our approach will consist of two steps: a) Proposing an explicit formulation of a covariant model and applying standard rules to relate a theory with its dual, and b) Implementing a projection of this covariant model to Horava–Lifshitz gravity using a gauge fixing condition. In this way we are able to present a dual action of the standard formulation of minimal linearized Horava–Lifshitz gravity.
Highlights
Electric-magnetic duality has emerged as a very interesting symmetry of diverse physical theories of increasing complexity, from zero to higher spin theories
For that end we proceeded in two steps: a) the construction of a covariant model that in an appropriate gauge reduce to Horava-Lifshitz gravity
We have used a gauge is fixing procedure that it breaks the full diffeomosphism grip of General Realtivity to a subgroup that coincides with the symmetry group of Horava-Lifshitz gravity., b) The implementation of parent action to construct the duality symmetry in a covariant model
Summary
Symmetries and variational principles play an essential role in the construction of interactions. The authors of [1, 2] proposed a variational formulation of the this duality, that works at the level of the equations of motion Even though this formulation is constructed giving up manifest spacetime covariance of the original Maxwell action the authors of [3] showed that in the case of linearized gravity it is possible to implement the electric-magnetic duality analogue at the level of an action. The interesting point about this duality is that Horava-Lifshitz gravity is not invariant under the complete spacetime diffeomorphisms but only under a subgroup of them This non full covariance is not an impediment to implement duality and is an example of the role played by the complementarity between covariance and duality. 28 114012 (Preprint 1101.1081) 2 [5] P Horava and C M Melby-Thompson 2010 Physical Review D 82 064027 URL http://link.aps.org/doi/. Ser. 314 012002 (Preprint 1103.5587) 2 [25] Charmousis C, Niz G, Padilla A and Saffin P M 2009 Journal of High Energy Physics 2009 070 ISSN
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