Path integral representation for Wilson loops and the non-Abelian Stokes theorem

Faber, M.; Ivanov, A. N.; Troitskaya, N. I.; Zach, Martin

doi:10.1103/physrevd.62.025019

Cited by 26 publications

(50 citation statements)

References 30 publications

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“…(6.117c) 57 For another choice of h 2 = − ν 2 , the same results are obtained if the following replacement is performed.…”

Section: Explicit Construction For Su(3)supporting

confidence: 66%

“…Rather, we claim that even in the SU(N) Yang-Mills theory a single magnetic monopole is sufficient to achieve confinement, when quarks belong to the fundamental representation of the color gauge group. In fact, this scenario was originally proposed in [59,60,61] based on a consideration from a non-Abelian Stokes theorem for the Wilson loop operator [55,56,57,58], which is more elaborated in [62,63,64,65] (See [66,67,68,69,70,71,72] for other versions of non-Abelian Stokes theorem). In order to consider confinement of quarks in the specified representation based on the Wilson loop operator, we adopt the color field n(x) taking the value in the Lie algebra of G/H, 14) whereH is a subgroup of G called the maximal stability subgroup which is determined once the highest-weight state of a given representation is chosen.…”

Section: 3)mentioning

confidence: 99%

“…Thus, imposing simultaneously two minimizing conditions removes the SU(N) ambiguity 57)and the color field configuration are decided as…”

Section: Lattice Reduction Condition and Color Fieldmentioning

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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“…(6.117c) 57 For another choice of h 2 = − ν 2 , the same results are obtained if the following replacement is performed.…”

Section: Explicit Construction For Su(3)supporting

confidence: 66%

Section: 3)mentioning

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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“…This work was all done using a Newtonian or modified Newtonian approach (by including gravitational radiation reaction in different ways in the calculations), and we note that the thermodynamic details are of little importance for the emission of gravitational waves, since it is concernced primarily with the motion of bulk matter at high densities. More recently, there have been advances in making post-Newtonian calculations of initial conditions (Lombardi, Rasio & Shapiro 1997) and mergers (Faber & Rasio 2000;Faber, Rasio & Manor 2000;Ayal et al 2001), and also in including general relativity (Wilson, Mathews & Marronetti 1996;Baumgarte et al 1997;Oohara & Nakamura 1999;Shibata 1999;Shibata & Uryū 2000;Usui, Uryū & Eriguchi 2000;Gourgoulhon et al 2001).…”

Section: Introduction a N D M O T I Vat I O Nmentioning

confidence: 99%

Newtonian hydrodynamics of the coalescence of black holes with neutron stars - IV. Irrotational binaries with a soft equation of state

Lee

2001

Monthly Notices of the Royal Astronomical Society

115

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We present the results of three‐dimensional hydrodynamical simulations of the final stages of in‐spiral in a black hole–neutron star binary, when the separation is comparable to the stellar radius. We use a Newtonian smooth particle hydrodynamics (SPH) code to model the evolution of the system, and take the neutron star to be a polytrope with a soft (adiabatic indices and equation of state and the black hole to be a Newtonian point mass. The only non‐Newtonian effect we include is a gravitational radiation back reaction force, computed in the quadrupole approximation for point masses. We use irrotational binaries as initial conditions for our dynamical simulations, which are begun when the system is on the verge of initiating mass transfer and followed for approximately 23 ms. For all the cases studied we find that the star is disrupted on a dynamical time‐scale, and forms a massive accretion torus around the spinning (Kerr) black hole. The rotation axis is clear of baryons (less than 10−5 M⊙ within 10°) to an extent that would not preclude the formation of a relativistic fireball capable of powering a cosmological gamma‐ray burst. Some mass (the specific amount is sensitive to the stiffness of the equation of state) may be dynamically ejected from the system during the coalescence and could undergo r‐process nucleosynthesis. We calculate the waveforms, luminosities and energy spectra of the gravitational radiation signal, and show how they reflect the global outcome of the coalescence process.

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“…This confirms fully the results obtained in Refs. [2,3] that the evolution operator Z Reg (R 2 , R 1 ) vanishes and the path integral representation of the Wilson loop suggested by Diakonov and Petrov in terms of the evolution operator Z Reg (R 2 , R 1 ) is erroneous. All of these statements are completely applicable to the results discussed by Diakonov and Petrov in their recent manuscript hep-lat/0008004 [4].…”

mentioning

confidence: 99%

On the Evaluation of the Evolution Operator Z Reg(R 2,R 1) in the Diakonov–Petrov Approach to the Wilson Loop

2006

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Path integral representation for Wilson loops and the non-Abelian Stokes theorem

Cited by 26 publications

References 30 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

Newtonian hydrodynamics of the coalescence of black holes with neutron stars - IV. Irrotational binaries with a soft equation of state

On the Evaluation of the Evolution Operator Z Reg(R 2,R 1) in the Diakonov–Petrov Approach to the Wilson Loop

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