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Register a new userSpontaneous Non-Hermiticity in Nambu-Jona-Lasinio model
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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.
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The formalism of Riemannian geometry is applied to study the phase transitions in Nambu -Jona Lasinio (NJL) model. Thermodynamic geometry reliably describes the phase diagram, both in the chiral limit and for finite quark masses. The comparison between the geometrical study of NJL model and of (2+1) Quantum Chromodynamics at high temperature and small baryon density shows a clear connection between chiral symmetry restoration/breaking and deconfinement/confinement regimes.
A novel strategy to handle divergences typical of perturbative calculations is implemented for the Nambu--Jona-Lasinio model and its phenomenological consequences investigated. The central idea of the method is to avoid the critical step involved in the regularization process, namely the explicit evaluation of divergent integrals. This goal is achieved by assuming a regularization distribution in an implicit way and making use, in intermediary steps, only of very general properties of such regularization. The finite parts are separated of the divergent ones and integrated free from effects of the regularization. The divergent parts are organized in terms of standard objects which are independent of the (arbitrary) momenta running in internal lines of loop graphs. Through the analysis of symmetry relations, a set of properties for the divergent objects are identified, which we denominate consistency relations, reducing the number of divergent objects to only a few ones. The calculational strategy eliminates unphysical dependencies of the arbitrary choices for the routing of internal momenta, leading to ambiguity-free, and symmetry-preserving physical amplitudes. We show that the imposition of scale properties for the basic divergent objects leads to a critical condition for the constituent quark mass such that the remaining arbitrariness is removed. The model become predictive in the sense that its phenomenological consequences do not depend on possible choices made in intermediary steps. Numerical results are obtained for physical quantities at the one-loop level for the pion and sigma masses and pion-quark and sigma-quark coupling constants.
Based on the Cornwall-Jackiw-Tomboulis effective potential, we extensively study nonperturbative renormalization of the gauged Nambu-Jona-Lasinio model in the ladder approximation with standing gauge coupling. Although the pure Nambu-Jona-Lasinio model is not renormalizable, presence of the gauge interaction makes it possible that the theory is renormalized as an interacting continuum theory at the critical line in the ladder approximation. Extra higher dimensional operators (``counter terms) are not needed for the theory to be renormalized. By virtue of the effective potential approach, the renormalization (``symmetric renormalization) is performed in a phase-independent manner both for the symmetric and the spontaneously broken phases of the chiral symmetry. We explicitly obtain $beta$ function having a nontrivial ultraviolet fixed line for the renormalized coupling as well as the bare one. In both phases the anomalous dimension is very large ($ ge 1$) without discontinuity across the fixed line. Operator product expansion is explicitly constructed, which is consistent with the large anomalous dimension owing to the appearance of the nontrivial extra power behavior in the Wilson coefficient for the unit operator. The symmetric renormalization breaks down at the critical gauge coupling, which is cured by the generalized renormalization scheme (``$tM$-dependent renormalization). Also emphasized is the formal resemblance to the four-fermion theory in less than four dimensions which is renormalizable in $1/N$ expansion.
The critical phenomena in strongly interaction matter are generally investigated using the mean-field model and are characterized by well defined critical exponents. However, such models provide only average properties of the corresponding order parameters and neglect altogether their possible fluctuations. Also the possible long range effect are neglected in the mean field approach. Here we investigate the critical behavior in the nonextensive version of the Nambu Jona-Lasinio model (NJL). It allows to account for such effects in a phenomenological way by means of a single parameter $q$, the nonextensivity parameter. In particular, we show how the nonextensive statistics influence the region of the critical temperature and chemical potential in the NJL mean field approach.
In this paper we discuss Nambu-Jona-Lasinio model as a classical model for dynamical mass generation and symmetry breaking. In addition we discuss the possible supersymmetric extensions of this model resulting from interaction terms with four chiral superfields that may be regarded as a supersymmetric generalization of the four-fermion interactions of the Nambu-Jona-Lasinio model. A four-superfield interaction terms can be constructed as either dimension 6 or dimension 5 operators. Through analyzing solutions to the gap equations, we discuss the dynamical generation of superfield Dirac mass, including a supersymmetry breaking part. A dynamical symmetry breaking generally goes along with the dynamical mass generation, for which a bi-superfield condensate is responsible.
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