Kramers-Moyall cumulant expansion for the probability distribution of parallel transporters in quantum gauge fields

Buividovich, P. V.; Kuvshinov, V. A.

doi:10.1103/physrevd.73.094015

Cited by 3 publications

(8 citation statements)

References 25 publications

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“…In [11] it was shown that the most general form of the diffusion equation for the probability distribution of the holonomies g [C] on the gauge group manifold is:…”

Section: Free Random Walks On the Group Manifoldmentioning

confidence: 99%

“…The term with first-order derivative is prohibited in ( 5) by gauge invariance. It was shown in [11] that the coefficients η a1...a k [C] are directly related to the cumulants of the shifted curvature tensor F a µν , which are the basic objects in the method of field correlators [4]. This relation can be formally written as [11]:…”

Section: Free Random Walks On the Group Manifoldmentioning

confidence: 99%

“…The statement about the singular field configurations can be formulated more precisely using the equations ( 6) and (11), which relate the step distribution P [g; C], the coefficients η a1...a k [C] and the cumulants of the shifted curvature tensor of Yang-Mills fields. The coefficients η a1...a k [C] can be calculated if the field configurations which contribute to the cumulants in (6) are known.…”

Section: Thin Center Vorticesmentioning

confidence: 99%

“…. It can be shown that p [g; C] is the Wilson loop in the regular representation of the gauge group [10,11].…”

Section: Introductionmentioning

confidence: 99%

“…In [11] the most general form of the diffusion equation for p [g; C] was obtained using the classical loop equations [14] and the cumulant expansion theorem [15]. It turned out that this diffusion equation should have the form of the so-called Kramers-Moyall cumulant expansion, which describes a free random walk with an arbitrary distribution of steps.…”

Section: Introductionmentioning

confidence: 99%

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Random walks of Wilson loops in the screening regime

Buividovich

Polikarpov

2008

Nuclear Physics B

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Dynamics of Wilson loops in pure Yang-Mills theories is analyzed in terms of random walks of the holonomies of the gauge field on the gauge group manifold. It is shown that such random walks should necessarily be free. The distribution of steps of these random walks is related to the spectrum of string tensions of the theory and to certain cumulants of Yang-Mills curvature tensor. It turns out that when colour charges are completely screened, the holonomies of the gauge field can change only by the elements of the group center, which indicates that in the screening regime confinement persists due to thin center vortices. Thick center vortices are also considered and the emergence of such stepwise changes in the limits of infinitely thin vortices and infinitely large loops is demonstrated.Comment: Major revision of the previous version, to appear in Nucl. Phys. B (10 pages RevTeX, 3 figures

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“…In [11] it was shown that the most general form of the diffusion equation for the probability distribution of the holonomies g [C] on the gauge group manifold is:…”

Section: Free Random Walks On the Group Manifoldmentioning

confidence: 99%

Section: Free Random Walks On the Group Manifoldmentioning

confidence: 99%

Section: Thin Center Vorticesmentioning

confidence: 99%

“…. It can be shown that p [g; C] is the Wilson loop in the regular representation of the gauge group [10,11].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Random walks of Wilson loops in the screening regime

Buividovich

Polikarpov

2008

Nuclear Physics B

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Color confinement and random matrices. A random walk down group manifold toward Casimir scaling

Bergner,

Gautam,

Hanada

2024

J. High Energ. Phys.

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We explain the microscopic origin of linear confinement potential with the Casimir scaling in generic confining gauge theories. In the low-temperature regime of confining gauge theories such as QCD, Polyakov lines are slowly varying Haar random modulo exponentially small corrections with respect to the inverse temperature, as shown by one of the authors (M. H.) and Watanabe. With exact Haar randomness, computation of the two-point correlator of Polyakov loops reduces to the problem of random walk on group manifold. Linear confinement potential with approximate Casimir scaling except at short distances follows naturally from slowly varying Haar randomness. With exponentially small corrections to Haar randomness, string breaking and loss of Casimir scaling at long distance follow. Hence we obtain the Casimir scaling which is only approximate and holds only at intermediate distance, which is precisely needed to explain the results of lattice simulations. For (1 + 1)-dimensional theories, there is a simplification that admits the Casimir scaling at short distances as well.

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Wilson loops and random matrices

Bergner,

Gautam,

Hanada

et al. 2024

J. High Energ. Phys.

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Linear confinement with Casimir scaling of the string tension in confining gauge theories is a consequence of a certain property of the Polyakov loop related to random matrices. This mechanism does not depend on the details of the theories (neither the gauge group nor dimensions) and explains approximate Casimir scaling below string-breaking length. In this paper, we study 3d SU(2) pure Yang-Mills theory numerically and find the same random-matrix behavior for rectangular Wilson loops. We conjecture that this is a universal feature of strongly coupled confining gauge theories.

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Kramers-Moyall cumulant expansion for the probability distribution of parallel transporters in quantum gauge fields

Cited by 3 publications

References 25 publications

Random walks of Wilson loops in the screening regime

Random walks of Wilson loops in the screening regime

Color confinement and random matrices. A random walk down group manifold toward Casimir scaling

Wilson loops and random matrices

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