Spontaneous Non-Hermiticity in Nambu-Jona-Lasinio model

TL;DR

This paper investigates how the Nambu-Jona-Lasinio model can spontaneously develop a non-Hermitian, PT-symmetric ground state through dynamical anti-Hermitian interactions, revealing new symmetry-breaking phenomena.

Contribution

It introduces the concept of spontaneous non-Hermiticity in the NJL model and analyzes the emergence and breaking of a noncompact non-Hermitian symmetry group.

Findings

NH ground state exhibits spontaneous symmetry breaking in both regimes

Inhomogeneous NH ground state at strong coupling in the chiral limit

NH ground state is spatially uniform at weak coupling, at the PT phase boundary

Abstract

We explore the physical consequences of a scenario when the standard Hermitian Nambu--Jona-Lasinio (NJL) model spontaneously develops a non-Hermitian PT-symmetric ground state via dynamical generation of an anti-Hermitian Yukawa coupling. We demonstrate the emergence of a noncompact non-Hermitian (NH) symmetry group which characterizes the NH ground state. We show that the NH group is spontaneously broken both in weak- and strong-coupling regimes. In the chiral limit at strong coupling, the NH ground state develops inhomogeneity, which breaks the translational symmetry. At weak coupling, the NH ground state is a spatially uniform state, which lies at the boundary between the PT-symmetric and PT-broken phases. Outside the chiral limit, the minimal NJL model does not possess a stable non-Hermitian ground state.