Curvature and topological effects on dynamical symmetry breaking in a four- and eight-fermion interaction model

TL;DR

This paper investigates how curvature, size, and topology influence symmetry breaking in a four- and eight-fermion interaction model, providing phase boundary calculations in curved and topologically non-trivial space-times.

Contribution

It introduces a detailed analysis of symmetry breaking mechanisms considering finite curvature, size, and topology effects in a prototype fermion interaction model.

Findings

Explicit phase boundary calculations in curved space-time.

Demonstrates effects of topology on symmetry breaking.

Provides insights relevant to GUT era physics.

Abstract

A dynamical mechanism for symmetry breaking is investigated under the circumstances with the finite curvature, finite size and non-trivial topology. A four- and eight-fermion interaction model is considered as a prototype model which induces symmetry breaking at GUT era. Evaluating the effective potential in the leading order of the 1/N-expansion by using the dimensional regularization, we explicitly calculate the phase boundary which divides the symmetric and the broken phase in a weakly curved space-time and a flat space-time with non-trivial topology, $R^{D-1} \otimes S^1$.