Symmetry breaking and restoration for interacting scalar and gauge fields in Lifshitz type theories

TL;DR

This paper investigates how anisotropic Lifshitz-type theories with scalar and gauge fields exhibit symmetry breaking at zero temperature and symmetry restoration at high temperature, revealing phase transition behaviors.

Contribution

It provides the first detailed analysis of one-loop effective potential in Lifshitz theories with both scalar and gauge fields at finite temperature.

Findings

Symmetry breaking occurs at zero temperature due to quantum effects.

Symmetry is restored at high temperature via a first-order phase transition.

The phase transition behavior depends on the relative coupling strengths.

Abstract

We consider the one-loop effective potential at zero and finite temperature in field theories with anisotropic space-time scaling, with critical exponent $z=2$, including both scalar and gauge fields. Depending on the relative strength of the coupling constants for the gauge and scalar interactions, we find that there is a symmetry breaking term induced at one-loop at zero temperature and we find symmetry restoration through a first-order phase transition at high temperature.