Derivation of the exact NSVZ β-function in SQED, regularized by higher derivatives, by direct summation of Feynman diagrams

Stepanyantz, K. V.

doi:10.1016/j.nuclphysb.2011.06.018

Cited by 86 publications

(188 citation statements)

References 72 publications

Supporting

Mentioning

175

Contrasting

Unclassified

Order By: Relevance

“…The integrals defining the three-loop β-function are presented, for example, in Ref. [55]. They were obtained in [47], but a more compact form for writing them was proposed later.…”

Section: (This Expression Is Written In the Euclidean Space After Tmentioning

confidence: 99%

NSVZ scheme with the higher derivative regularization for SQED

2013

Self Cite

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

“…The integrals defining the three-loop β-function are presented, for example, in Ref. [55]. They were obtained in [47], but a more compact form for writing them was proposed later.…”

Section: (This Expression Is Written In the Euclidean Space After Tmentioning

confidence: 99%

NSVZ scheme with the higher derivative regularization for SQED

2013

Self Cite

View full text Add to dashboard Cite

show abstract

“…With the higher covariant derivative regularization the NSVZ relation was derived for the Abelian supersymmetric theories in all orders for the renormalization group (RG) functions defined in terms of the bare coupling constant [34,35] (which are scheme-independent for a fixed regularization [36]). The RG functions defined in the standard way in terms of the renormalized coupling constant [37] satisfy the NSVZ relation only in the NSVZ scheme which in this case can be constructed in all orders by imposing simple boundary conditions on the renormalization constants [20,36].…”

Section: Jhep05(2016)014mentioning

confidence: 99%

“…The main feature of quantum corrections, which allows to do this, is the factorization of integrals for the β-function (defined in terms of the bare coupling constant) into integrals of (double) total derivatives in the momentum space in the limit of the vanishing external momentum [38,39]. In the Abelian case this has been proved in all orders [34,35] and confirmed by explicit calculations in the three-loop approximation [40]. Using a similar method it has been proved that the integrals for the Adler D-function [41] (defined in terms of the bare coupling constant) in N = 1 supersymmetric QCD are also integrals of double total derivatives in all orders.…”

Section: Jhep05(2016)014mentioning

confidence: 99%

“…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 more important reason for making the one-loop calculation is that for deriving the NSVZ relation by the direct summation of supergraphs in all orders (such as in refs. [34,35]) this approximation should be considered separately and the BRST invariant regularization is highly desirable. This paper is organized as follows.…”

Section: Jhep05(2016)014mentioning

confidence: 99%

See 2 more Smart Citations

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.

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

The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities

Stepanyantz

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

The contributions of the matter superfields and of the Faddeev-Popov ghosts to the βfunction of N = 1 supersymmetric gauge theories defined in terms of the bare couplings are calculated in all orders in the case of using the higher covariant derivative regularization. For this purpose we use the recently proved statement that the β-function in these theories is given by integrals of double total derivatives with respect to the loop momenta. These integrals do not vanish due to singularities of the integrands. This implies that the β-function beyond the one-loop approximation is given by the sum of the singular contributions, which is calculated in all orders for singularities produced by the matter superfields and by the Faddeev-Popov ghosts. The result is expressed in terms of the anomalous dimensions of these superfields. It coincides with the corresponding part of the new form of the NSVZ equation, which can be reduced to the original one with the help of the non-renormalization theorem for the triple gauge-ghost vertices.

show abstract

Derivation of the exact NSVZ β-function in SQED, regularized by higher derivatives, by direct summation of Feynman diagrams

Cited by 86 publications

References 72 publications

NSVZ scheme with the higher derivative regularization for SQED

NSVZ scheme with the higher derivative regularization for SQED

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

The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities

Contact Info

Product

Resources

About