Effective potential for Lifshitz type z=3 gauge theories

TL;DR

This paper calculates the one-loop effective potential in Lifshitz-type z=3 gauge theories, revealing symmetry breaking effects and multiple local minima influenced by scalar, fermion, and gauge field interactions.

Contribution

It provides the first detailed analysis of the one-loop effective potential in anisotropic z=3 gauge theories including scalar, fermion, and gauge fields.

Findings

Fermion determinant induces symmetry breaking at one loop.

A local minimum appears at non-zero scalar field for all Yukawa couplings.

Multiple local minima depend on the relative strengths of coupling constants.

Abstract

We consider the one-loop effective potential at zero temperature in field theories with anisotropic space-time scaling, with critical exponent $z=3$, including scalar, fermion and gauge fields. The fermion determinant generates a symmetry breaking term at one loop in the effective potential and a local minimum appears, for non zero scalar field, for every value of the Yukawa coupling. Depending on the relative strength of the coupling constants for the scalar and the gauge field, we find a second symmetry breaking local minimum in the effective potential for a bigger value of the scalar field.