Dynamical symmetry breaking and space-time topology

Abstract

Vacuum polarization and spontaneous symmetry breaking in a two-dimensional massless fermion field theory with quartic interactions (the Gross-Neveu model) are studied in a cylindrical ( R ' x S ' ) space-time topology. In the case of untwisted fermion fields the symmetry-breaking behavior is similar to the model in Minkowski space-time except that the location of the effective potential minima depends upon the size of the space. In the case of a twisted fermion field there exists a critical size of the space such that the symmetry breaking occurs only for space larger than the critical one.

Properties of the massive Gross-Neveu model with nonzero baryon and isospin chemical potentials

“…In our previous paper [26] the phase diagram of the (1 þ 1)-dimensional GN model with two massless quark flavors was investigated under the constraint that quark matter occupies a finite space volume (see also the relevant papers [27]). In particular, the charged pion condensation phenomenon in cold quark matter with zero baryonic density, i.e., at ¼ 0, but nonzero isotopic density, i.e., with nonzero isospin chemical potential I , was studied there in the large N c -limit.…”

Finite size effects in the Gross-Neveu model with isospin chemical potential

“…Due to their relative simplicity in the leading order of a large N c -expansion (N c is a number of colored quarks), it is very convenient to use GN models for considering such a phenomenon of dense QCD as color superconductivity [16,18] and to elaborate new nonperturbative methods of quantum field theory [19,20,21]. Moreover, the influence of the space compactification on chiral symmetry breaking both in the vacuum (µ B = 0) [22] and in dense baryon matter (µ B = 0) [23] was studied in terms of GN models (see also the appropriate papers [24,25,26]). …”

CHARGED PION CONDENSATION PHENOMENON OF DENSE BARYONIC MATTER INDUCED BY FINITE VOLUME: THE NJL2 MODEL CONSIDERATION

“…Finally, note that the above results, obtained both in the periodic and antiperiodic cases, refer strictly to the case ν > 0. A detailed study of GN-type models in spacetime with nontrivial topology in the case of µ = 0, ν = 0 was made in [33].…”

“…Thus, the effects inherent for real dense quark matter, such as color superconductivity (spontaneous breaking of the continuous color symmetry) or charged pion condensation (spontaneous breaking of the continuous isospin symmetry) might be simulated in terms of a simpler (1+1)-dimensional GN-type model, though only in the leading order of the large N c approximation (see, e.g., [26,30] and [31,32], respectively). Finally, one should recall that both the chiral phase transition [33] and color superconductivity [30] were investigated in the framework of GN models with account of the nontrivial R 1 × S 1 spacetime topology. In general, this paper is devoted to the consideration of the charged pion condensation phenomenon under the influence of finite-size effects.…”