Lorentz breaking terms from Einstein gravity

Abstract

We construct an action which is invariant under the foliation preserving diffeomorphism from the Einstein Hilbert action. Starting from the Einstein Hilbert action, we introduce the gauge invariance under the anisotropic rescaling by using the Stückelberg method. We then introduce the gauge field corresponds to the anisotropic rescaling, and the Stückelberg field turns out to be the Nambu-Goldstone boson. The Nambu-Goldstone boson, however, is not completely eaten by the massive gauge field and the Nambu-Goldstone boson can be integrated out from the action. Then the resultant action is a Horava-Lifshitz type action which contains $R^3$ term.

arXiv comment11 pages

References in corpus (9)

• Massive Gravity
• Gravity Duals of Lifshitz-like Fixed Points
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• A healthy extension of Horava gravity
• Non-relativistic holography
• Strong coupling in Horava gravity
• Renormalization of Horava Gravity
• Power counting renormalizability of quantum gravity in Lifshitz spacetime
• Power counting renormalizability of scalar theory in Lifshitz spacetime