Matter in Horava-Lifshitz gravity

TL;DR

This paper investigates matter's role in Horava-Lifshitz gravity, analyzing classical matter Lagrangians and quantum corrections, revealing issues with light cone modifications and potential higher derivatives affecting UV completeness.

Contribution

It provides a detailed analysis of matter coupling in non-projectable Horava-Lifshitz gravity at both classical and quantum levels, highlighting constraints and quantum corrections.

Findings

Classical matter Lagrangians must reduce to relativistic form to avoid sourcing Stuckelberg fields.

Large quantum corrections to the light cone at low energies due to matter coupling.

Potential generation of higher order time derivatives raises concerns about UV completeness.

Abstract

We consider the role of matter in the non-projectable version of Horava-Liftshitz gravity at both a classical and a quantum level. At the classical level, we construct general forms of matter Lagrangians consistent with the reduced symmetry group and demonstrate that they must be reduced to their relativistic form if they are to avoid sourcing the gravitational Stuckelberg field. At the quantum level we consider one loop corrections to the propagator for a relativistic scalar minimally coupled to gravity at tree level. We find large corrections to the light cone at low energies arising from the strength of the coupling of the scalar graviton to matter. We also find evidence that higher order time derivatives may be generated, which is worrying if this is to be taken seriously as a UV complete theory.