Gribov Problem for Gauge Theories: A Pedagogical Introduction

Esposito, Giampiero; Pelliccia, Diego N.; Zaccaria, F.

doi:10.1142/s0219887804000216

Cited by 24 publications

(26 citation statements)

References 51 publications

(79 reference statements)

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“…Naively, one could expect to completely avoid the Gribov problem by simply choosing algebraic gauge fixings like the axial gauge or the temporal gauge, which are free of Gribov copies. However, these choices have their own, and even worse, problems 1 (for a detailed reviews see [4] [5]). Here it is just worth mentioning one serious issue: any loop computation in the algebraic gauge-fixings mentioned above are very difficult already beyond two-loop.…”

Section: Introductionmentioning

confidence: 99%

The Gribov problem in presence of background field for SU(2) Yang–Mills theory

2016

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The Gribov problem in the presence of a background field is analyzed: in particular, we study the Gribov copies equation in the Landau-De Witt gauge as well as the semi-classical Gribov gap equation. As background field, we choose the simplest non-trivial one which corresponds to a constant gauge potential with non-vanishing component along the Euclidean time direction. This kind of constant non-Abelian background fields is very relevant in relation with (the computation of) the Polyakov loop but it also appears when one considers the non-Abelian Schwinger effect. We show that the Gribov copies equation is affected directly by the presence of the background field, constructing an explicit example. The analysis of the Gribov gap equation shows that the larger the background field, the smaller the Gribov mass parameter. These results strongly suggest that the relevance of the Gribov copies (from the path integral point of view) decreases as the size of the background field increases. * canfora@cecs.cl † dhidalgo@cecs.cl ‡ pais@cecs.cl arXiv:1610.08067v2 [hep-th]

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Section: Introductionmentioning

confidence: 99%

The Gribov problem in presence of background field for SU(2) Yang–Mills theory

2016

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“…However, beyond perturbation theory, gauge conditions like the Landau-gauge condition (6) have no longer a unique solution for a given configuration. There are several explicit examples illustrating this fact [18,[45][46][47][48]. Such independent solutions are called Gribov copies, and the associated ambiguity of the gauge condition is termed the Gribov-Singer ambiguity [18,19].…”

Section: Non-perturbative Gauge-fixing and Gribov Copiesmentioning

confidence: 99%

“…In the perturbative expansion of a renormalizable theory, like Yang-Mills theory, it can be shown that this is possible with a finite number of independent renormalization constants. For covariant gauges, like the Landau gauge, this is equivalent to multiplying correlation functions by appropriate chosen renormalization factors 47 , at least as long as no matter fields are involved. If this is also possible beyond perturbation theory has not yet been proven, though no evidence to the contrary exists.…”

Section: Renormalizationmentioning

confidence: 99%

Gauge bosons at zero and finite temperature

2013

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Gauge theories of the Yang-Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary.Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity, which requires the introduction of non-local constraints. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the single most important first step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion.After gauge-fixing, it is possible to study gauge bosons in detail. The most direct access is provided by their correlation functions. The corresponding two-and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, particle-like properties at high energies, and the running coupling. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras.Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan-Boltzmann type. The resolution of this apparent contradiction is also presented. In addition, this resolution provides an explicit and constructive solution to the Linde problem.Thus, the technical and conceptual framework presented here can be taken as a basis how to determine correlation functions in Yang-Mills theory, therefore opening up the avenue to investigate theories of direct practical relevance. The status of this effort will be briefly described, alongside with connections to other approaches to Yang-Mills theory beyond perturbation theory.

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“…In the nonperturbative regime, the Faddeev-Popov trick for covariant gauges does therefore not correspond to inserting a ''1'' into the functional integral, instead one inserts a ''0'', making the functional integral ill-defined, [66]. In gravity, the Gribov problem has been discussed in [67][68][69]. We observe an interesting alteration to the standard problem in our setting: At locations in metric configuration space where the simple FP determinant would be zero, the additional terms in the ghost action, which will in general depend on the background metric and the matter fields, need not be zero.…”

Section: Gribov Problem and Nonperturbative Structure Of The Ghostmentioning

confidence: 99%

Faddeev-Popov ghosts in quantum gravity beyond perturbation theory

Eichhorn¹

2013

Phys. Rev. D

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We study the Faddeev-Popov ghost sector of asymptotically safe quantum gravity, which becomes non-perturbative in the ultraviolet. We point out that nonzero matter-ghost couplings and higher-order ghost self-interactions exist at a non-Gaussian fixed point for the gravitational couplings, i.e., in the ultraviolet. Thus the ghost sector in this non-perturbative ultraviolet completion does not keep the structure of a simple Faddeev-Popov determinant. We discuss implications of the new ghost couplings for the Renormalization Group flow in gravity, the form of the ultraviolet completion, and the relevant couplings, i.e., free parameters, of the theory.Comment: 12 pages, 7 figures, version identical to published version in PR

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Gribov Problem for Gauge Theories: A Pedagogical Introduction

Cited by 24 publications

References 51 publications

The Gribov problem in presence of background field for SU(2) Yang–Mills theory

The Gribov problem in presence of background field for SU(2) Yang–Mills theory

Gauge bosons at zero and finite temperature

Faddeev-Popov ghosts in quantum gravity beyond perturbation theory

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