General Covariance in Gravity at a Lifshitz Point

TL;DR

The paper investigates gravity with Lifshitz-type anisotropic scaling, exploring its theoretical structure and potential connections to lattice approaches like CDT through the spectral dimension behavior.It then constructs a gravity theory with an extended gauge symmetry, incorporating an Abelian gauge field and a Newton prepotential to realize nonrelativistic general covariance and remove the scalar graviton while preserving tensor modes.In the infrared, the model yields a Schwarzschild-like solution and GR-like tensor dynamics, suggesting compatibility with solar-system tests, but requires careful handling of Lorentz invariance and additional fields in the phenomenology.Overall, the work shows a viable path toward GR-like IR behavior within Lifshitz gravity, while highlighting open questions about the interpretation and constraints of the extended gauge sector and the role of the Newton prepotential.

Abstract

This paper is based on the invited talks delivered by the author at GR 19: the 19th International Conference on General Relativity and Gravitation, Ciudad de México, México, July 2010. In Part 1, we briefly review some of the main features of quantum gravity with anisotropic scaling, and comment on its possible relation to the causal dynamical triangulations (CDT) approach to lattice quantum gravity. Part 2 explains the construction of gravity with anisotropic scaling with an extended gauge symmetry -- essentially a nonrelativistic version of general covariance. This extra symmetry eliminates the scalar graviton polarization, and thus brings the theory closer to general relativity at long distances.

Figures (2)

• Figure 1: The mean-field phase diagram of the Lifshitz scalar theory (\ref{['sldef']}).
• Figure 2: The mean-field phase diagram of gravity with anisotropic scaling in $2+1$ dimensions with the compact spatial slices $\Sigma=S^2$.