Chiral symmetry breaking in gauged ${\bf NJL}$ model in curved spacetime

TL;DR

This paper investigates chiral symmetry breaking in the gauged NJL model within curved spacetime using RG methods, deriving the effective potential and critical curvature for symmetry breaking, with implications for GUTs.

Contribution

It introduces a novel RG improved effective potential for the gauged NJL model in curved spacetime and explicitly determines the curvature threshold for chiral symmetry breaking.

Findings

Derived the RG improved effective potential in curved spacetime.

Explicitly obtained the curvature at which chiral symmetry breaks.

Established equivalence with ladder Schwinger-Dyson equations in curved spacetime.

Abstract

Using the renormalization group (RG) approach and the equivalency between the class of gauge-Higgs-Yukawa models and the gauged Nambu-Jona-Lasinio (NJL) model, we study the gauged NJL model in curved space-time. The behaviour of the scalar-gravitational coupling constant $\xi(t)$ in both theories is discussed. The RG improved effective potential of gauged NJL model in curved spacetime is found. The curvature at which chiral symmetry in the gauged NJL model is broken is obtained explicitly in a remarkably simple form. The powerful RG improved effective potential formalizm leads to the same results as ladder Schwinger-Dyson equations which have not been formulated yet in curved spacetime what opens new possibilities in the study of GUTs and NJL-like models in curved spacetime.