Generalized dual symmetry of nonabelian theories, monopoles and dyons

Abstract

In the present talk we present an investigation of nonabelian SU(N) gauge theories, describing a system of fields with non--dual g and dual \tilde g charges and revealing the generalized dual symmetry. The Zwanziger type action is suggested. The renormalization group equations for pure nonabelian theories, in particular for pure SU(3)\times\widetilde{SU(3)} gauge theory (as an example) are analysed. We consider not only monopoles, but also dyons. The behaviour of the QCD total beta--function is investigated. It was shown that this beta--function is antisymmetric under the interchange α\leftrightarrow\frac 1α(here α\equivα_s), and has zero ("fixed point") at α= 1. Monopoles, or dyons, are responsible for the phase transition. Considering critical points at α_1\approx 0.4 and α_2\approx 2.5, we give an explanation of the freezing of α_s.

15 pages, 5 figures, Presented at the 12th Lomonosov Conference on Elementary Particle Physics, Moscow State University, Moscow, 25-31 August, 2005