Pauli-Villars regularization for non-Abelian gauge theories

Slavnov, A. A.

doi:10.1007/bf01036595

Cited by 125 publications

(167 citation statements)

References 3 publications

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“…The concrete implementation of such regularization introduced by Slavnov in Ref. [3] (see also Ref. [4] for a review) encounters, however, two problems.…”

Section: Introductionmentioning

confidence: 99%

“…Although higher loop diagrams acquire by power counting a negative superficial divergent dimension, the divergences of one loop diagrams are not smoothed by higher covariant derivatives [1] [2]. One way of getting rid of the remaining one loop divergences could be the introduction of an additional gauge invariant Pauli-Villars regularization [3] (see also [2]). The concrete implementation of such regularization introduced by Slavnov in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Consistency of the regularization of gauge theories by high covariant derivatives

Asorey¹,

Falceto²

1996

Phys. Rev. D

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We show that regularization of gauge theories by higher covariant derivatives and gauge invariant Pauli-Villars regulators is a consistent method if the Pauli-Villars vector fields are considered in a covariant α-gauge with α = 0 and a given auxiliary preregularization is introduced in order to uniquely define the regularization. The limit α → 0 in the regulating Pauli-Villars fields is pathological and the original Slavnov proposal in covariant Landau gauge is not correct because of the appearance of massless modes in the regulators which do not decouple when the ultraviolet regulator is removed. In such a case the method does not correspond to the regularization of a pure gauge theory but that of a gauge theory in interaction with massless ghost fields. However, a minor modification of Slavnov method provides a consistent regularization even for such a case. The regularization that we introduce also solves the problem of overlapping divergences in a way similar to geometric regularization and yields the standard values of the β and γ functions of the renormalization group equations.

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“…The concrete implementation of such regularization introduced by Slavnov in Ref. [3] (see also Ref. [4] for a review) encounters, however, two problems.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Consistency of the regularization of gauge theories by high covariant derivatives

Asorey¹,

Falceto²

1996

Phys. Rev. D

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“…By introducing the higher derivative term one regularizes divergences beyond the oneloop approximation [71]. In order to get rid of the remaining one-loop divergences, it is necessary to insert the Pauli-Villars determinants into the generating functional [72]. Due to the absence of quadratic divergences in supersymmetric theories it is possible to use the following Pauli-Villars determinants:…”

Section: Adjmentioning

confidence: 99%

One-loop divergences in non-Abelian supersymmetric theories regularized by BRST-invariant version of the higher derivative regularization

Aleshin

Kazantsev

Skoptsov

et al. 2016

J. High Energ. Phys.

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We consider a general non-Abelian renormalizable N = 1 supersymmetric gauge theory, regularized by higher covariant derivatives without breaking the BRST invariance, and calculate one-loop divergences for a general form of higher derivative regulator and of the gauge fixing term. It is demonstrated that the momentum integrals giving the one-loop β-function are integrals of double total derivatives independently of a particular choice of the higher derivative term. Evaluating them we reproduce the well-known result for the one-loop β-function. Also we find that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in the considered approximation.

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“…For cancellation of remaining one-loop divergences the coefficients c I should satisfy the conditions [57] I c I = 1;…”

Section: Introductionmentioning

confidence: 99%

“…Then the divergences remain only in the one-loop approximation [56]. According to the standard prescription they should be regularized by inserting the Pauli-Villars determinants into the generating functional [57]:…”

Section: Introductionmentioning

confidence: 99%

NSVZ scheme with the higher derivative regularization for SQED

2013

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The exact NSVZ relation between a β-function of N = 1 SQED and an anomalous dimension of the matter superfields is studied within the Slavnov higher derivative regularization approach. It is shown that if the renormalization group functions are defined in terms of the bare coupling constant, this relation is always valid. In the renormalized theory the NSVZ relation is obtained in the momentum subtraction scheme supplemented by a special finite renormalization. Unlike the dimensional reduction, the higher derivative regularization allows to fix this finite renormalization. This is made by imposing the conditions Z 3 (α, µ = Λ) = 1 and Z(α, µ = Λ) = 1 on the renormalization constants of N = 1 SQED, where Λ is a parameter in the higher derivative term. The results are verified by the explicit three-loop calculation. In this approximation we relate the DR scheme and the NSVZ scheme defined within the higher derivative approach by the finite renormalization.

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Pauli-Villars regularization for non-Abelian gauge theories

Cited by 125 publications

References 3 publications

Consistency of the regularization of gauge theories by high covariant derivatives

Consistency of the regularization of gauge theories by high covariant derivatives

One-loop divergences in non-Abelian supersymmetric theories regularized by BRST-invariant version of the higher derivative regularization

NSVZ scheme with the higher derivative regularization for SQED

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