Non-Abelian dual superconductivity in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>Yang-Mills theory: Dual Meissner effect and type of the vacuum

Shibata, Akihiro; Kondo, Keiichi; Kato, Seikou; Shinohara, T.

doi:10.1103/physrevd.87.054011

Cited by 22 publications

(19 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…32 In preceding works, the equipollent gauge transformation was called the gauge transformation II or the active or background gauge transformation. 33 This does not means that the solution is unique. Other new field variables are also obtained from the original A µ (x) by change of variables thanks to the existence of the color field.…”

Section: Change Of Variablesmentioning

confidence: 99%

“…the SU(3) Yang-Mills theory in the minimal option. These results are based on the lattice reformulation of SU(3) Yang-Mills theory constructed in [30,31] and the results of numerical simulations on the lattice performed in [32,33].…”

Section: 3)mentioning

confidence: 99%

“…33 For the moment, therefore, we do not ask how this is achieved and we omit the subscript A of n [A ] to simplify the notation. 31 It was pointed out that the single color field is enough for specifying the Wilson loop operator through the non-Abelian Stokes theorem [60].…”

Section: Change Of Variablesmentioning

confidence: 99%

“…In other words, the first method can be regarded as a gauge-fixed version of the second method. The second method including the extension to SU(N) explained later has been furthermore developed especially in the last decade by the Chiba University group [18,19,20,24] and Chiba/KEK/Fukui (Takamatsu) collaborations [25,26,27,28,29,30,31,32,33].…”

Section: 3)mentioning

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%

See 4 more Smart Citations

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

et al. 2015

Self Cite

View full text Add to dashboard Cite

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...

show abstract

Section: Change Of Variablesmentioning

confidence: 99%

Section: 3)mentioning

confidence: 99%

Section: Change Of Variablesmentioning

confidence: 99%

Section: 3)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

et al. 2015

Self Cite

View full text Add to dashboard Cite

show abstract

Setting the string shoving picture in a new frame

Bierlich

Chakraborty

Gustafson

et al. 2021

J. High Energ. Phys.

View full text Add to dashboard Cite

Based on the recent success of the Angantyr model in describing multiplicity distributions of the hadronic final state in high energy heavy ion collisions, we investigate how far one can go with a such a string-based scenario to describe also flow effects measured in such collisions.For this purpose we improve our previous so-called shoving model, where strings that are close in space-time tend to repel each other in a way that could generate anisotropic flow, and we find that this model can indeed generate such flows in AA collisions. The flow generated is not quite enough to reproduce measurements, but we identify some shortcomings in the presented implementation of the model that, when fixed, could plausibly give a more realistic amount of flow.

show abstract

Nonperturbative quantization ‘a la Heisenberg for non-Abelian gauge theories: two-equation approximation. Applications: a flux tube solution and a scalar model of glueball

Dzhunushaliev

2017

EPJ Web Conf.

View full text Add to dashboard Cite

Abstract. The nonperturbative quantization technique à la Heisenberg is applied for the SU(3) gauge theory. The operator Yang-Mills equation and corresponding infinite set of equations for all Green's functions are considered. Gauge degrees of freedom are splitted into two groups:Using some assumptions about 2-and 4-point Green's functions, the infinite set of equations is truncated to two equations. The first equation is the S U(2)× U(1) Yang-Mills equation, and the second equation describes a gluon condensate formed by coset fields. A flux tube solution describing longitudinal color electric fields stretched between quark and antiquark located at the ± infinities is obtained. It is shown that the dual Meissner effect appears in this solution: the electric field is pushed out from the gluon condensate.

show abstract

Non-Abelian dual superconductivity inSU(3)Yang-Mills theory: Dual Meissner effect and type of the vacuum

Cited by 22 publications

References 59 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

Setting the string shoving picture in a new frame

Nonperturbative quantization ‘a la Heisenberg for non-Abelian gauge theories: two-equation approximation. Applications: a flux tube solution and a scalar model of glueball

Contact Info

Product

Resources

About