General Covariance in Quantum Gravity at a Lifshitz Point

TL;DR

This paper explores extending gauge symmetry in Lifshitz-type quantum gravity to eliminate extra scalar modes, aligning the theory more closely with general relativity at large scales.

Contribution

It introduces a local U(1) symmetry extension that removes the scalar graviton and enforces relativistic coupling constants in Lifshitz gravity.

Findings

Scalar graviton is eliminated with U(1) extension.

Coupling constant λ is fixed to 1.

Theory reproduces general relativity features at long distances.

Abstract

In the minimal formulation of gravity with Lifshitz-type anisotropic scaling, the gauge symmetries of the system are foliation-preserving diffeomorphisms of spacetime. Consequently, compared to general relativity, the spectrum contains an extra scalar graviton polarization. Here we investigate the possibility of extending the gauge group by a local U(1) symmetry to "nonrelativistic general covariance." This extended gauge symmetry eliminates the scalar graviton, and forces the coupling constant $\lambda$ in the kinetic term of the minimal formulation to take its relativistic value, $\lambda=1$. The resulting theory exhibits anisotropic scaling at short distances, and reproduces many features of general relativity at long distances.