Dynamical symmetry breaking in curved spacetime -review-

TL;DR

This review explores how four-fermion interaction models exhibit dynamical symmetry breaking in curved spacetime, analyzing phase transitions induced by curvature, temperature, topology, and magnetic fields, with applications in quantum gravity.

Contribution

It provides a comprehensive overview of recent developments in understanding dynamical symmetry breaking in four-fermion models within curved spacetime, including phase transition mechanisms and gravitational effects.

Findings

Curvature induces phase transitions in fermion mass generation.

Magnetic fields may be counteracted by gravitational effects to restore symmetry.

Applications in quantum gravity highlight the models' relevance.

Abstract

Four-fermion interaction models are considered to be prototype models for dynamical symmetry breaking.The present review deals with recent developments in the studies of dynamical symmetry breaking in the four-fermion interaction models and their extension in curved spacetime. Starting with the Minkowski spacetime in dimension $D$ ($2 \leq D \leq 4$) the effective potential in the leading order of $1/N$-expansion is calculated and the phase structure of the theory is investigated. In curved spacetime curvature-induced phase transitions are discussed in the circumstances where fermion masses are dynamically generated. Subsequently a possibility of curvature- and temperature-induced or curvature- and topology-induced phase transitions is discussed. It is also argued that the chiral symmetry broken by a weak magnetic field may be restored due to the presence of gravitational field. Finally some applications of four-fermion models in quantum gravity are briefly described.