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arXiv · 1604.08054

Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity

Jelle Hartong·Yang Lei·Niels A. Obers
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Abstract

We show that certain three-dimensional Horava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various non-relativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schroedinger algebra each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Horava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Horava-Lifshitz gravity with a local U(1) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schroedinger algebra containing 3 extra generators that are central with respect to the subalgebra of Galilean boosts, momenta and rotations, for which the Chern-Simons theory gives rise to a novel version of non-projectable conformal Horava-Lifshitz gravity that we refer to as Schroedinger gravity. This theory has a z=2 Lifshitz geometry as a vacuum solution and thus provides a new framework to study Lifshitz holography.

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Jelle Hartong, Yang Lei, Niels A. Obers. 2016-05-12. Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity. https://doi.org/10.1103/physrevd.94.065027

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