Nambu-Jona-Lasinio Model in Curved Space-Time

TL;DR

This paper investigates how space-time curvature influences the phase structure of the Nambu-Jona-Lasinio model, revealing a first-order phase transition and providing a phase diagram based on curvature and coupling constants.

Contribution

It introduces a calculation of the effective potential in curved space-time using the Schwinger proper-time method, demonstrating the impact of curvature on phase transitions in the model.

Findings

First-order phase transition induced by curvature change

Dynamical fermion mass depends on curvature and coupling

Phase diagram mapped in curvature-coupling space

Abstract

The phase structure of Nambu-Jona-Lasinio model with N-component fermions in curved space-time is studied in the leading order of the 1/N expansion. The effective potential for composite operator $\bar{\psi}\psi$ is calculated by using the normal coordinate expansion in the Schwinger proper-time method. The existence of the first-order phase transition caused by the change of the space-time curvature is confirmed and the dynamical mass of the fermion is calculated as a simultaneous function of the curvature and the four-fermion coupling constant. The phase diagram in the curvature and the coupling constant is obtained.