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.
Highlights
The Nambu–Jona-Lasinio (NJL) model [1] describes the dynamics of interacting relativistic fermions
The model is often employed as a viable low-energy effective theory of quantum chromodynamics (QCD) because the NJL model, to QCD, exhibits both the dynamical mass gap generation and the axial symmetry breaking
We elaborated the physical consequences of a scenario in which the standard Hermitian Nambu–Jona-Lasinio model spontaneously develops a non-Hermitian PT -symmetric ground state
Summary
The Nambu–Jona-Lasinio (NJL) model [1] describes the dynamics of interacting relativistic fermions. A fireball of QGP is a relativistically expanding out-of-equilibrium system This system does not reside in a steady regime, the fermionic interactions may generate a non-Hermitian ground state in a steady-state nonequilibrium regime, which is realized in between the early moments of the plasma until the evolution of the QGP approaches the chiral crossover and eventual hadronization. Some problems known to reside in the strongly coupling regime have been investigated when nonHermitian terms are considered These are the case, for example, of the Kondo effect [22], the out-of-equilibriuminduced coupling between the Higgs mode and the Leggett modes in driven superconductors [23], or the Kibble-Zurek mechanism in non-Hermitian environments [24]. The Appendix contains the presentation of the gradient expansion of the effective non-Hermitian action with the nonhomogeneous terms included
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