Symmetry breaking and restoration in Lifshitz type theories

TL;DR

This paper investigates the one-loop effective potential in Lifshitz scalar theories with anisotropic scaling, revealing symmetry breaking at zero temperature and symmetry restoration at high temperature for z=2, and complex behavior for z=3.

Contribution

It provides the first detailed analysis of symmetry breaking and restoration in Lifshitz theories with different dynamical critical exponents at one-loop level.

Findings

Symmetry breaking occurs at zero temperature for z=2.

Symmetry restoration happens at high temperature for z=2.

No clear symmetry breaking effects for z=3 with positive mass term.

Abstract

We consider the one-loop effective potential at zero and finite temperature in scalar field theories with anisotropic space-time scaling. For $z=2$, 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. For $z=3$, we considered at first the case with a positive mass term at tree level and found no symmetry breaking effects induced at one-loop, and then we study the case with a negative mass term at tree level where we cannot conclude about symmetry restoration effects at high temperature because of the imaginary parts that appear in the effective potential for small values of the scalar field.