Gribov ambiguities in the maximal Abelian gauge

Dudal, David; Capri, M. A. L.; Gracey, J.A.; Lemes, V. E. R.; Sobreiro, R. F.; Sorella, S. P.; Thibes, Ronaldo; Verschelde, Henri

doi:10.1590/s0103-97332007000200025

Cited by 16 publications

(9 citation statements)

References 24 publications

(69 reference statements)

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“…There are two notable examples of gauge choices which also possess a Hermitean Faddeev-Popov operator: the maximal Abelian and Coulomb gauges. For such gauges, an explicit construction of the Gribov-Zwanziger action and its refinement was performed, see [48][49][50][51][52][53][54][55][56][57][58][59][60][61]. In spite of this fact, these gauges have their own peculiarities and the development of the refined Gribov-Zwanziger scenario for them is not at the same level as in the Landau gauge.…”

Section: The Gribov Problem In the Landau Gaugementioning

confidence: 99%

A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

et al. 2017

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In this work, we study the propagators of matter fields within the framework of the refined GribovZwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the FaddeevPopov operator is added in the matter sector.

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Section: The Gribov Problem In the Landau Gaugementioning

confidence: 99%

A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

et al. 2017

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“…within the same Landau gauge condition for the Faddeev-Popov action adopted to lattice calculations. For the sake of completeness, notice the study [14] of the Gribov problem (beyond the Landau gauge) in covariant R ξ gauges for a small value of the gauge parameter ξ for an approximation of the quantum action being quadratic in the fields; let us also notice the proposal of a new form of the horizon functional in R ξ gauges [15] in the maximal Abelian gauges [16], [17], in the Coulomb gauge [18], and on a curved Riemannian background to study the influence of the curvature tensor on changing the size of the Gribov region [19].…”

Section: Introductionmentioning

confidence: 99%

On gauge independence for gauge models with soft breaking of BRST symmetry

Reshetnyak

2014

Int. J. Mod. Phys. A

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A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field-antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional S-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang-Mills and gravity theories. The Gribov-Zwanziger action and the refined Gribov-Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.

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“…For contemporary considerations, justified by lattice calculations of Gribov copies, see, e.g., [76,77,78]. For applications of the Gribov-Zwanziger theory in the Coulomb, Landau and maximal Abelian gauges, as well as in covariant R ξ -gauges in the pure Yang-Mills theory, see [79,80,81,82,83,84,85,86,87,88]. Notice that there exist other approaches intended to eliminate (or bypass) the Gribov ambiguity problem: first, the procedure of imposing an algebraic (instead of differential) gauge on auxiliary scalar fields in a theory which is non-perturbatively equivalent to the Yang-Mills theory [89,90,91], second, the procedure of averaging over the Gribov copies with a non-uniform weight in the path integral and the replica trick [92,93], third, the incorporation of the Gribov factor (restricting the functional measure in the path integral to the first Gribov region) into the Faddeev-Popov matrix, thereby modifying the gauge algebra of gauge transformations [34].…”

Section: Relating Gauges In Standard Model and Gribov Ambiguitymentioning

confidence: 99%

Finite field-dependent BRST–anti-BRST transformations: Jacobians and application to the Standard Model

Moshin

Reshetnyak

2016

Int. J. Mod. Phys. A

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We continue our research Nucl.Phys B888, 92 (2014); Int. J. Mod. Phys. A29, 1450159 (2014); Phys. Lett. B739, 110 (2014); Int. J. Mod. Phys. A30, 1550021 (2015) and extend the class of finite BRST-antiBRST transformations with odd-valued parameters λa, a = 1, 2, introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST-antiBRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST-antiBRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST-antiBRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits non-trivial solutions leading to a Jacobian equal to unity. Finite BRST-antiBRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters λa is obtained, providing the equivalence of path integrals in any 3-parameter R ξ -like gauges. The Gribov-Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in R ξ -like gauges, in a gauge-independent way using field-dependent BRST-antiBRST transformations, and in R ξ -like gauges using transverse-like non-Abelian gauge fields.Recently, in the articles [1,2,3,4], we have proposed an extension of BRST-antiBRST transformations [5,6,7,8] to the case of finite (both global and field-dependent) parameters for Yang-Mills and general gauge theories in the framework of the generalized Hamiltonian [9, 10] -see also 13,14] BRST-antiBRST quantization schemes. The idea of "finiteness" incorporates into finite transformations a new term being quadratic in the transformation parameters λ a , thereby lifting BRST-antiBRST transformations from the algebraic level to the * moshin@rambler.ru † reshet@ispms.tsc.ru 1 group level, which has been discussed also in [15,16]. BRST transformations [17,18,19] in both the Lagrangian [20,21] and generalized Hamiltonian [19, 22, 23] quantization schemes -described by a single odd-valued parameter µ and trivially lifted from the algebraic formwith ← − s 2 = 0, in view of the nilpotency property µ 2 = 0 -have first been suggested in Yang-Mills theories for fielddependent parameters in [24,25]; see also [26,27]. The introduction of such transformations is based on a functional equation for the infinitesimal parameter, providing the invariance of the integrand of the vacuum functional (in the path integral representation based on the Faddeev-Popov rules [28...

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Gribov ambiguities in the maximal Abelian gauge

Cited by 16 publications

References 24 publications

A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

On gauge independence for gauge models with soft breaking of BRST symmetry

Finite field-dependent BRST–anti-BRST transformations: Jacobians and application to the Standard Model

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