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Hamiltonian analysis of nonprojectable Hořava-Lifshitz gravity with U(1) symmetry

Shinji Mukohyama1,2, Ryo Namba2, Rio Saitou1,3, and Yota Watanabe2,*

  • 1Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
  • 2Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
  • 3Institute for Cosmic Ray Research, The University of Tokyo, Kashiwa, Chiba 277-8582, Japan

  • *Corresponding author. yota.watanabe@ipmu.jp
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Phys. Rev. D 92, 024005 – Published 2 July, 2015

DOI: https://doi.org/10.1103/PhysRevD.92.024005

Abstract

We study the nature of constraints and count the number of degrees of freedom in the nonprojectable version of the U(1) extension of Hořava-Lifshitz gravity, using the standard method of Hamiltonian analysis in the classical field theory. This makes it possible for us to investigate the condition under which the scalar graviton is absent at a fully nonlinear level. We show that the scalar graviton does not exist at the classical level if and only if two specific coupling constants are exactly zero. The operators corresponding to these two coupling constants are marginal for any values of the dynamical critical exponent of the Lifshitz scaling and thus should be generated by quantum corrections even if they are eliminated from the bare action. We thus conclude that the theory in general contains the scalar graviton.

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Phys. Rev. D 92, 024005– Published 2 July, 2015
  • Received 28 April 2015

© 2015 American Physical Society

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