Factorization of Integrals Defining the β-Function into Integrals of Total Derivatives in N=1 SQED, Regularized by Higher Derivatives

Stepanyantz, K. V.

doi:10.1007/s10773-011-0905-9

Cited by 14 publications

(16 citation statements)

References 58 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…(1.3) is equal to the number of loops L in the original supergraph, while the number of momentum integrations in the right hand side is equal to L − 1. Some explicit calculations made with the higher derivative regularization have demonstrated that the integrals in the left hand side are integrals of total derivatives [39,51] and even of double total derivatives [40,43,53,54,56]. Due to this feature it is possible to calculate one of the momentum integrals and obtain the same number of momentum integrations in both sides of eq.…”

Section: Jhep04(2018)130mentioning

confidence: 99%

New form of the exact NSVZ β-function: the three-loop verification for terms containing Yukawa couplings

Kazantsev

Shakhmanov

Stepanyantz

2018

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We investigate a recently proposed new form of the exact NSVZ β-function, which relates the β-function to the anomalous dimensions of the quantum gauge superfield, of the Faddeev-Popov ghosts, and of the chiral matter superfields. Namely, for the general renormalizable N = 1 supersymmetric gauge theory, regularized by higher covariant derivatives, the sum of all three-loop contributions to the β-function containing the Yukawa couplings is compared with the corresponding two-loop contributions to the anomalous dimensions of the quantum superfields. It is demonstrated that for the considered terms both new and original forms of the NSVZ relation are valid independently of the subtraction scheme if the renormalization group functions are defined in terms of the bare couplings. This result is obtained from the equality relating the loop integrals, which, in turn, follows from the factorization of the integrals for the β-function into integrals of double total derivatives. For the renormalization group functions defined in terms of the renormalized couplings we verify that the NSVZ scheme is obtained with the higher covariant derivative regularization supplemented by the subtraction scheme in which only powers of ln Λ/µ are included into the renormalization constants.

show abstract

Section: Jhep04(2018)130mentioning

confidence: 99%

New form of the exact NSVZ β-function: the three-loop verification for terms containing Yukawa couplings

Kazantsev

Shakhmanov

Stepanyantz

2018

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Subsequently, the results of the papers [44,45] were written in the form of integrals of double total derivatives [46][47][48]. However, the versions of the higher covariant derivative regularization which were used for making explicit calculations for the non-Abelian N = 1 supersymmetric theories break the BRST invariance [49,50] (while the background gauge invariance is not broken).…”

Section: Jhep05(2016)014mentioning

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.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…We choose masses of the Pauli-Villars fields so that they will be proportional to the parameter Λ in the higher derivative term [50,55]:…”

Section: Introductionmentioning

confidence: 99%

NSVZ scheme with the higher derivative regularization for SQED

2013

View full text Add to dashboard Cite

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.

show abstract

Factorization of Integrals Defining the β-Function into Integrals of Total Derivatives in N=1 SQED, Regularized by Higher Derivatives

Abstract: Some calculations in supersymmetric theories, made with the higher derivative regularization, show that the β-function is given by integrals of total derivatives. This is qualitatively explained for the N = 1 supersymmetric electrodynamics in all orders.

Cited by 14 publications

References 58 publications

New form of the exact NSVZ β-function: the three-loop verification for terms containing Yukawa couplings

New form of the exact NSVZ β-function: the three-loop verification for terms containing Yukawa couplings

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

Contact Info

Product

Resources

About