A new classical solution of the Yang-Mills field equations

Alfaro, V. de; Fubini, S.; Furlan, G.

doi:10.1016/0370-2693(76)90022-8

Cited by 313 publications

(203 citation statements)

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“…See also [164,165,166,167,168] for relationships among various topological objects. In the course of studying the relationship between Abelian magnetic monopoles and center vortices [48], merons [174] are recognized as an important object [113,114,170]. Merons [174,175,178] are solutions of the Yang-Mills field equation and are characterized by one half topological charge, i.e., having half-integer Pontryagin index.…”

Section: Brief History Before Our Workmentioning

confidence: 99%

“…In the course of studying the relationship between Abelian magnetic monopoles and center vortices [48], merons [174] are recognized as an important object [113,114,170]. Merons [174,175,178] are solutions of the Yang-Mills field equation and are characterized by one half topological charge, i.e., having half-integer Pontryagin index. These configurations escaped from the above consideration, since they have infinite action due to their singular behaviors.…”

Section: Brief History Before Our Workmentioning

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: Brief History Before Our Workmentioning

confidence: 99%

Section: Brief History Before Our Workmentioning

confidence: 99%

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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“…Some years ago, in fact, de Alfaro et al [27] described a spherically symmetric singular solution to the classical Yang-Mills equations on fiat four-dimensional euclidean space with a (nonabelian) magnetic field that is well suited to support a wormhole. Their solution, which became known as a "meron", has much in common with the singular monopole solutions of gauge theories in three-dimen-sional euclidean space.…”

Section: Magnetic Wormholes In 3 + 1 Dimensionsmentioning

confidence: 99%

Magnetic wormholes and topological symmetry

et al. 1990

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We investigate the wormhole solutions that arise in the semiclassical analysis of euclidean gravity coupled to gauge fields. In 2 + 1 dimensions, "magnetic monopole" solutions can be constructed, for either abelian or nonabelian gauge fields. The low-energy physics induced by these wormholes qualitatively resembles, but is quantitatively distinguishable from, the tow-energy physics of a gauge theory (without wormholes) that undergoes the Higgs mechanism at the wormhole mass scale. Wormholes are suppressed if matter fields are introduced that transform suitably under the gauge group. In 3 + 1 dimensions, "meron'" solutions can be constructed, for nonabelian gauge fields only. We argue, however, that these wormhole solutions do not contribute to the semiclassical evaluation of the path integral.

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“…Translated into the instanton-vacuum language, the renormalizability of the QCD implies that the probability that there are N I's andĪ's in the vacuum is [7,27] 39) where N ≃ V F a µν F a µν /(32π 2 ) is the average number of I's andĪ's .…”

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Instantons at work

Diakonov

2003

Progress in Particle and Nuclear Physics

351

506

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The aim of this review is to demonstrate that there exists a coherent picture of strong interactions, based on instantons. Starting from the first principles of Quantum Chromodynamics -via the microscopic mechanism of spontaneous chiral symmetry breakingone arrives to a quantitative description of the properties of light hadrons, with no fitting parameters. The discussion of the importance of instanton-induced interactions in soft high-energy scattering is new.

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A new classical solution of the Yang-Mills field equations

Cited by 313 publications

References 3 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

Magnetic wormholes and topological symmetry

Instantons at work

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