Dynamical mass generation and confinement in two-dimensional gauge theories

Abstract

Operator solutions are used to study non-perturbative aspects of two-dimensional models, with quartic fermionic interactions, internal SU( N)-flavor and SU( M) diagonal color index. The models exhibit dynamical mass generation. Bosonization aspects of the chiral SU( M) Gross-Neveu model are considered. Off-diagonal SU( M) current conservation emerges as a quantum property. Dynamical mass generation is accomplished by the appearance of M − 1 zero-mode excitations. These M − 1 “would-be” Goldstone bosons are screened by the introduction of M − 1 “gluon” fields in the “torus” of the SU( M) group. The consequent vacuum condensation of these free charges allows for 〈θ a| ΨΨ|θ a〉 ≠ 0 . As the screened charges are free, the theories decouple and no additional confinement aspects appear. However, if the gauge fields are introduced such that the screened charges are not free, then additional confinement aspects will be present. The hamiltonian term responsible for the quartic fermionic interaction and consequently for the dynamical mass generation plays, within the confinement aspects, an analogous role to that which is played by a mass term explicitly introduced in the theory. Quarks with screened “diagonal color” are liberated only for some special “θ-worlds”.