Dynamical symmetry breaking in curved spacetime -review-

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.