Generalized dual symmetry of non-Abelian theories and the freezing of alpha(s)

摘要

The quantum Yang-Mills theory, describing a system of fields with nondual (chromoelectric g) and dual (chromomagnetic) charges and revealing the generalized dual symmetry, is developed by analogy with the Zwanziger formalism in QED. The renormalization group equations (RGE's) for pure non-Abelian theories axe analyzed for both constants, alpha = g(2)/4 pi and alpha = (g) over tilde (2)/4 pi. The pure SU(3) x SU(3) gauge theory is investigated as an example. We consider not only monopoles, but also dyons. The behavior of the total SU(3) beta-function is investigated in the whole region of alpha equivalent to alpha(s) : 0 < alpha < infinity. It is shown that this beta-function is antisymmetric under the interchange alpha -> 1/alpha and is given by the well-known perturbative expansion not only for a < 1, but also for alpha 1. Using an idea of the Maximal Abelian Projection by 't Hooft, we have considered the formation of strings - the ANO flux tubes - in the Higgs model of scalar monopole (or dyon) fields. In this model we have constructed the behavior of the beta-function in the vicinity of the point a = 1, where it acquires a zero value. Considering the phase transition points at alpha approximate to 0.4 and alpha approximate to 2.5, we give the explanation of the freezing of a.. The evolution of alpha(-1)(s) (mu) with energy scale 14 and the behavior of V-eff(mu) axe investigated for both, perturbative and nonperturbative regions of QCD. It was shown that the effective potential has a minimum, ensured by the dual sector of QCD. The gluon condensate F-0(2), corresponding to this minimum, is predicted: F-0(2) approximate to 0.15 GeV4, in agreement with the well-known results.