Searches for self-consistent vacuum states of a gluon field

In the present talk we present an investigation of nonabelian SU (N ) gauge theories, describing a system of fields with non-dual g and dualg 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) × 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 ↔ 1 α (here α ≡ α s ), and has zero ("fixed point") at α = 1. Monopoles, or dyons, are responsible for the phase transition. Considering critical points at α 1 ≈ 0.4 and α 2 ≈ 2.5, we give an explanation of the freezing of α s .

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“…For dyons -particles having both, electric and magnetic, charges simultaneouslywe have in Eqs. (90)(91)(92)(93)(94)(95)(96)(97)(98):…”

Section: Nonabelian Theories With Matter Fieldsmentioning

confidence: 99%

“…The nature of gluon condensate was investigated in a lot of papers (for example, very interesting considerations were given in Refs. [90,91]). The value of gluon condensate was estimated in Refs.…”

Section: Nonabelian Theories With Matter Fieldsmentioning

confidence: 99%

Generalized Dual Symmetry of Nonabelian Theories, Monopoles and Dyons

Das¹,

Лаперашвили²,

Nielsen³

2006

Particle Physics at the Year of 250th Anniversary of Moscow University

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

Das

Лаперашвили

Nielsen³

2006

Int. J. Mod. Phys. A

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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.

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Searches for self-consistent vacuum states of a gluon field

Cited by 2 publications

References 8 publications

Generalized Dual Symmetry of Nonabelian Theories, Monopoles and Dyons

Generalized Dual Symmetry of Nonabelian Theories, Monopoles and Dyons

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

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Searches for self-consistent vacuum states of a gluon field

Cited by 2 publications

References 8 publications

Generalized Dual Symmetry of Nonabelian Theories, Monopoles and Dyons

Generalized Dual Symmetry of Nonabelian Theories, Monopoles and Dyons

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

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