New Heat Kernel Method in Lifshitz Theories

TL;DR

This paper introduces a novel covariant heat kernel technique tailored for Lifshitz theories, enabling systematic analysis of renormalization flows while preserving covariance, and demonstrates its effectiveness through anomaly calculations.

Contribution

A new covariant heat kernel method for Lifshitz theories that handles scalar and spin operators, improving the study of renormalization group flows.

Findings

Successfully computed the anisotropic Weyl anomaly in (2+1) dimensions.

Validated the method by reproducing known anomaly results.

Extended the approach to operators with spin in arbitrary dimensions.

Abstract

We develop a new heat kernel method that is suited for a systematic study of the renormalization group flow in Horava gravity (and in Lifshitz field theories in general). This method maintains covariance at all stages of the calculation, which is achieved by introducing a generalized Fourier transform covariant with respect to the nonrelativistic background spacetime. As a first test, we apply this method to compute the anisotropic Weyl anomaly for a (2+1)-dimensional scalar field theory around a z=2 Lifshitz point and corroborate the previously found result. We then proceed to general scalar operators and evaluate their one-loop effective action. The covariant heat kernel method that we develop also directly applies to operators with spin structures in arbitrary dimensions.