GENERALIZED DUAL SYMMETRY OF NON-ABELIAN THEORIES AND THE FREEZING OF αs

Abstract

The quantum Yang–Mills theory, describing a system of fields with nondual (chromoelectric g) and dual (chromomagnetic [Formula: see text]) 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 are analyzed for both constants, α = g2/4π and [Formula: see text]. The pure [Formula: see text] gauge theory is investigated as an example. We consider not only monopoles, but also dyons. The behavior of the total SU(3) β-function is investigated in the whole region of α≡αs: 0≤α < ∞. It is shown that this β-function is antisymmetric under the interchange α ↔ 1/α and is given by the well-known perturbative expansion not only for α≪1, but also for α≫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 β-function in the vicinity of the point α = 1, where it acquires a zero value. Considering the phase transition points at α≈0.4 and α≈2.5, we give the explanation of the freezing of αs. The evolution of [Formula: see text] with energy scale μ and the behavior of V eff (μ) are 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 [Formula: see text], corresponding to this minimum, is predicted: [Formula: see text], in agreement with the well-known results.