Extended QCD versus Skyrme-Faddeev theory

Bae, W. S.; Cho, Y. M.; Kimm, Seung-Won

doi:10.1103/physrevd.65.025005

Cited by 74 publications

(98 citation statements)

References 27 publications

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“…Moreover, it tells one the necessity of adopting the reduction condition in the master Yang-Mills theory, although the conventional MA gauge is merely one choice of the gauge fixings. 23 In other words, the CDG-Yang-Mills theory has been constructed on a vacuum selected in a gauge invariant way among possible vacua of the master Yang-Mills theory, since the reduction condition is satisfied for the CDG field configurations realizing the minimum of the functional d D x 1 2 X 2 µ and the minimum min ω,θ d D x 1 2 X 2 µ is gauge invariant in the sense that it does no longer change the value with respect to the local gauge transformation. Therefore, the reduction condition is a gauge-invariant criterion of choosing a vacuum on which the CDG-Yang-Mills theory is defined from the vacua of the master Yang-Mills theory, although the reduction condition is not necessarily a unique prescription of selecting out the gauge-invariant vacuum.…”

Section: New Viewpoint For the Yang-mills Theory: Reduction From The mentioning

confidence: 99%

“…The coherent states |ξ, Λ are in one-to-one correspondence with the coset representatives ξ ∈ G/H: 23) and the coherent states preserve all the algebraic and topological properties of the coset space G/H. In other words, |ξ, Λ and ξ ∈ G/H are topologically equivalent.…”

mentioning

confidence: 99%

“…Keeping this question in mind, we proceed to extend the new formulation of SU(2) Yang-Mills theory to the SU(N) case. For the SU(N) Yang-Mills field, the decomposition as an extension of the CDGFN decomposition was proposed by Cho [21,23] and Fadeev-Niemi [22] which we call the Cho-Faddeev-Niemi (CFN) decomposition. They introduced N − 1 color direction fields n j (x) (j = 1, .…”

Section: 3)mentioning

confidence: 99%

“…However, this classification is not necessarily independent, leading to sometimes confusing and misleading results. 23 A possible algorithm for the numerical simulation was proposed in [108]. Moreover, the actual simulations were first attempted in [109].…”

Section: Gauge Transformation Of New Variablesmentioning

confidence: 99%

“…2. Field decomposition [14,15,16,17], [21,22,23] and change of variables [18,19,20], [24,25,26,27,28,29,30,31,32,33] It is possible to realize magnetic monopoles in the pure non-Abelian gauge theory in the absence of the adjoint Higgs field, without explicitly introducing singularities in the gauge connection and without breaking the original gauge symmetry and color symmetry. This is done by performing a gauge-covariant decomposition of the gluon field by introducing the local color direction field.…”

Section: Introductionmentioning

confidence: 99%

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Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

et al. 2015

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The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the YangMills theory based on change of variables extending the decomposition of the SU(N) Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the SU(N) Wilson loop operator.Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole.We show especially that magnetic monopoles in the Yang-Mills theory can be constructed in a manifestly gauge-invariant way starting from the gauge-invariant Wilson loop operator and thereby the contribution from the magnetic monopoles can be extracted from the Wilson loop in a gauge-invariant way through the non-Abelian Stokes theorem for the Wilson loop operator, which is a prerequisite for exhibiting magnetic monopole dominance for quark confinement. The Wilson loop average is calculated according to the new reformulation written in terms of new field variables obtained from the original Yang-Mills field based on change of variables. The Maximally Abelian gauge in the original Yang-Mills theory is also reproduced by taking a specific gauge fixing in the reformulated Yang-Mills theory. This observation justifies the preceding results obtained in the maximal Abelian gauge at least for gaugeinvariant quantities for SU(2) gauge group, which eliminates the criticism of gauge artifact raised for the Abelian projection. The claim has been confirmed based on the numerical simulations.However, for SU(N) (N ≥ 3), such a gauge-invariant reformulation is not unique, although the extension along the line proposed by Cho, Faddeev and Niemi is possible. In fact, we have found that there are a number of possible options of the reformulations, which are discriminated by the maximal stability 1 groupH of G, while there is a unique option ofH = U(1) for G = SU(2). The maximal stability group depends...

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Section: New Viewpoint For the Yang-mills Theory: Reduction From The mentioning

confidence: 99%

mentioning

confidence: 99%

Section: 3)mentioning

confidence: 99%

Section: Gauge Transformation Of New Variablesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

et al. 2015

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Nonlinearity and Topology

Saxena

Kevrekidis

Cuevas–Maraver

2020

Nonlinear Systems and Complexity

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The interplay of nonlinearity and topology results in many novel and emergent properties across a number of physical systems such as chiral magnets, nematic liquid crystals, Bose-Einstein condensates, photonics, high energy physics, etc. It also results in a wide variety of topological defects such as solitons, vortices, skyrmions, merons, hopfions, monopoles to name just a few. Interaction among and collision of these nontrivial defects itself is a topic of great interest. Curvature and underlying geometry also affect the shape, interaction and behavior of these defects. Such properties can be studied using techniques such as, e.g. the Bogomolnyi decomposition. Some applications of this interplay, e.g. in nonreciprocal photonics as well as topological materials such as Dirac and Weyl semimetals, are also elucidated.

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Nonabelian Faddeev-Niemi decomposition of the SU(3) Yang-Mills theory

Evslin

Giacomelli

Konishi

et al. 2011

J. High Energ. Phys.

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Faddeev and Niemi (FN) have introduced an abelian gauge theory which simulates dynamical abelianization in Yang-Mills theory (YM). It contains both YM instantons and Wu-Yang monopoles and appears to be able to describe the confining phase. Motivated by the meson degeneracy problem in dynamical abelianization models, in this note we present a generalization of the FN theory. We first generalize the Cho connection to dynamical symmetry breaking pattern SU(N + 1) -> U(N), and subsequently try to complete the Faddeev-Niemi decomposition by keeping the missing degrees of freedom. While it is not possible to write an on-shell complete FN decomposition, in the case of SU(3) theory of physical interest we find an off-shell complete decomposition for SU(3). U(2) which amounts to partial gauge fixing, generalizing naturally the result found by Faddeev and Niemi for the abelian scenario SU(N + 1) -> U(1) N. We discuss general topological aspects of these breakings, demonstrating for example that the FN knot solitons never exist when the unbroken gauge symmetry is nonabelian, and recovering the usual no-go theorems for colored dyons

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Extended QCD versus Skyrme-Faddeev theory

Cited by 74 publications

References 27 publications

Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

Nonlinearity and Topology

Nonabelian Faddeev-Niemi decomposition of the SU(3) Yang-Mills theory

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