Chiral Symmetry Breaking in the Nambu-Jona-Lasinio Model in Curved Spacetime with Non-Trivial Topology

TL;DR

This paper investigates how curvature and topology influence chiral symmetry breaking in the Nambu-Jona-Lasinio model, revealing phase transition types and calculating dynamical fermionic mass in curved spacetime with non-trivial topology.

Contribution

It provides a detailed analysis of the phase structure of the NJL model in curved spacetime with non-trivial topology, including the effects of curvature and topology on phase transitions and fermionic mass.

Findings

Second order phase transition at zero curvature and small radius of S^1.

Transition becomes first order as curvature increases or S^1 radius decreases.

Dynamical fermionic mass calculated in various geometric configurations.

Abstract

We discuss the phase structure (in the $1/N$-expansion) of the Nambu-Jona-Lasinio model in curved spacetime with non-trivial topology ${\cal M}^3 \times {\rm S}^1$. The evaluation of the effective potential of the composite field $\bar{\psi} \psi$ is presented in the linear curvature approximation (topology is treated exactly) and in the leading order of the $1/N$-expansion. The combined influence of topology and curvature to the phase transitions is investigated. It is shown, in particular, that at zero curvature and for small radius of the torus there is a second order phase transition from the chiral symmetric to the chiral non-symmetric phase. When the curvature grows and (or) the radius of ${\rm S}^1$ decreases, then the phase transition is in general of first order. The dynamical fermionic mass is also calculated in a number of different situations.