Nonrelativistic Chern-Simons theories and three-dimensional Hořava-Lifshitz gravity

Jelle Hartong, Yang Lei, and Niels A. Obers
Phys. Rev. D 94, 065027 – Published 22 September 2016

Abstract

We show that certain three-dimensional Hořava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various nonrelativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schrödinger algebras each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Hořava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Hořava-Lifshitz gravity with a local U(1) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schrödinger algebra containing three 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 nonprojectable conformal Hořava-Lifshitz gravity that we refer to as Chern-Simons Schrödinger gravity. This theory has a z=2 Lifshitz geometry as a vacuum solution and thus provides a new framework to study Lifshitz holography.

  • Received 6 June 2016

DOI:https://doi.org/10.1103/PhysRevD.94.065027

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Jelle Hartong1,*, Yang Lei2,†, and Niels A. Obers3,‡

  • 1Physique Théorique et Mathématique and International Solvay Institutes, Université Libre de Bruxelles, C.P. 231, 1050 Brussels, Belgium
  • 2Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road, Durham DH1 3LE, United Kingdom
  • 3The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark

  • *hartong@ulb.ac.be
  • yang.lei@durham.ac.uk
  • obers@nbi.ku.dk

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Issue

Vol. 94, Iss. 6 — 15 September 2016

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