On the regularization of Lifshitz-type field theories

TL;DR

This paper investigates the regularization and renormalization group flow of Lifshitz-type scalar field theories with anisotropic scaling, deriving the one-loop effective potential and beta functions using proper time regularization.

Contribution

It introduces a proper time regularization method for Lifshitz theories and analyzes their one-loop effective potential and RG flow in both IR and UV regimes.

Findings

Derived the regularized one-loop effective potential.

Analyzed the RG flow of the potential in different regimes.

Calculated the beta functions for the couplings.

Abstract

We consider Lifshitz-type scalar theories with explicit breaking of the Lorentz symmetry that, in addition, exhibit anisotropic scaling laws near the ultraviolet fixed point. Using the proper time regularization method on the spatial coordinates only, we derive the regularized form of the one-loop effective potential in such theories. We study the main features of the one-loop effective potential and, also, the RG flow of the scale-dependent potential both in the IR and UV regimes. The beta functions for the couplings are derived.