Competition of color ferromagnetic and superconductive states in a quark-gluon system

Abstract

The possibility of color ferromagnetism in an SU (2) gauge field model is investigated. The conditions allowing a stable color ferromagnetic state of the quark system in the chromomagnetic field occupying small domains are considered. A phase transition between this state and the color superconducting states is considered. The effect of finite temperature is analyzed.PACS numbers: 11.10. Wx, 11.30.Qc, 12.20.Ds, 12.60.Cn IntroductionNonperturbative effects of non-abelian gauge theories take place in the infrared region.Among such nonperturbative effects are the existence of the QCD vacuum with gluon and quark condensates, chiral symmetry breaking, confinement and the hadronization process.They can only be studied by approximate methods and in the framework of various effective models. For instance, one of the possibilities to approximately describe the gluon condensate is to introduce background color fields of certain configurations (see, e.g., [1,2]).Another example of nonperturbative problems is the physics of light mesons that can be described by effective four-fermion models such as the Nambu-Jona-Lasinio (NJL) quark model, which was successfully used to implement the ideas of dynamical chiral symmetry breaking (DχSB) and bosonization (see e.g. [3], [4] and references therein; for a review of (2+1)-dimensional four-quark effective models see [5]).In the framework of four-fermion models, it was shown that a constant magnetic field [6] induces the dynamical chiral symmetry breaking (DχSB), as well as the fermion mass 2 generation, even under conditions when the interaction between fermions is weak. This phenomenon of magnetic catalysis was explained basing upon the idea of effective reduction of space dimensionality in the presence of a strong external magnetic field [7] (see also paper[8] and references therein). It was also demonstrated that a strong chromomagnetic field catalyzes DχSB [9]. As was shown in [10], this effect can be understood in the framework of the dimensional reduction mechanism as well, and it does not depend on the particular form of the constant chromomagnetic field configuration.One of the solutions of the Yang-Mills equations that can serve as a model for the gluon condensate is a constant chromomagnetic field. Its role was demonstrated in [11,12]. In these papers, the authors calculated the one-loop effective potential for a constant chromomagnetic field B and they demonstrated that it reaches its minimum at a nonvanishing value of B.However this simple analytical model of the gluon condensate with a uniform chromomagnetic field B = const (the so-called "colour ferromagnetic state") [11,12] suffered from an instability [13]. This problem later has been studied in a number of papers. In particular, The principal difficulty in finding a stable color ferrromagnetic state is that a local minimum of the action can not be obtained, since the corresponding field configuration proved to be spatially inhomogeneous. In order to circumvent this difficulty, the method earlier applied in analy...

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