General covariance in quantum gravity at a Lifshitz point

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 $\ensuremath{\lambda}$ in the kinetic term of the minimal formulation to take its relativistic value, $\ensuremath{\lambda}=1$. The resulting theory exhibits anisotropic scaling at short distances, and reproduces many features of general relativity at long distances.