Covariant computation of effective actions in Horava-Lifshitz gravity

TL;DR

This paper develops a systematic method to compute heat-kernel coefficients for anisotropic operators in curved spacetime, deriving effective actions and analyzing the renormalization group flow in Horava-Lifshitz gravity.

Contribution

It introduces a covariant approach to compute heat-kernel coefficients for anisotropic Laplacians, advancing the understanding of quantum corrections in Horava-Lifshitz gravity.

Findings

Identified the Gaussian fixed point as a UV completion candidate.

Found the high-energy phase is screened by a Landau pole.

Derived beta functions and effective actions for the theory.

Abstract

We initiate the systematic computation of the heat-kernel coefficients for Laplacian operators obeying anisotropic dispersion relations in curved spacetime. Our results correctly reproduce the limit where isotropy is restored and special anisotropic cases considered previously in the literature. Subsequently, the heat kernel is used to derive the scalar-induced one-loop effective action and beta functions of Horava-Lifshitz gravity. We identify the Gaussian fixed point which is supposed to provide the UV completion of the theory. In the present setting, this fixed point acts as an infrared attractor for the renormalization group flow of Newton's constant and the high-energy phase of the theory is screened by a Landau pole. We comment on the consequences of these findings for the renormalizability of the theory.