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

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.

Are preons dyons? Naturalness of three generations

“…In our preonic model the group SU( 6) is broken by condensed Abelian scalar spreons belonging to the Cartan subalgebra U(1) 5 (compare with the results of Ref. [66]). Then for the one family of preons we have:…”

“…The values of α −1 (M crit ) and α −1 ( M crit ) can be calculated by the method developed in Refs. [65,66]. If the SU(N) group is broken by Abelian scalar particles belonging to its Cartan subalgebra U(1) N −1 , then the SU(N) critical coupling constant α crit N is given by the following expression in the one-loop approximation (see [65]):…”

Construction of a model of monopolium and its search via multiphoton channels at LHC

“…In the Zwanziger formulation, the degrees of freedom are doubled by the introduction of electric and magnetic vector potentials, but are halved by the projection to the η µ direction. Such a formulation in a non-Abelian gauge theory is more complicated but is possible [16,17,18]. If the axial gauge is taken,…”

Dyons Near the Planck Scale

“…Here we have used the Dirac relation for non-Abelian theories (see explanation in Ref. [13]): gg = 4πn, n ∈ Z, αα = 1.…”