Spontaneous non-Hermiticity in the Nambu–Jona-Lasinio model

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