NONPERTURBATIVE EFFECTS IN 2D CPN-1 MODEL AND 4D YM THEORY - A ZN TORON APPROACH

A lot of different problems such as: fractional topological charge, torons, Z(N)-symmetry, theta-dependence, confinement, U(1)-problem and all that are discussed in 2d CP(N-1) model and 4d gluodynamics. A comprehensive topological classification of torons (the toron is a self-dual solution with topological number Q = 1/N) is formulated and their interaction is founded in the quasiclassical approximation. It turns out that the number of different kinds of torons is equal to N, and that they are classified by the weights-mu of fundamental representation of the group SU(N). Moreover, an interaction of these torons is Coulomb-like approximately SIGMA(ij)mu(i)mu(j) ln(x(i) - x(j))2 and this gas can be expressed as a field theory of the Toda type. The expectation of different quantities (the vacuum energy, the topological density, the Wilson loop operator) are calculated using this effective field theory. All results (confinement, correct dependence on theta, and so on) are precisely what is well known from different considerations. The disorder parameter M is introduced and the corresponding vacuum expectation value is calculated [M] approximately exp(2-pi-ik/N) in agreement with 't Hooft's conjecture about properties of [M] in the confinement phase. The hypothesis of abelian dominance and corresponding Weyl Z(N) symmetry is realized in this approach in an automatic way.