K. V. Stepanyantz
Moscow State University
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Featured researches published by K. V. Stepanyantz.
Theoretical and Mathematical Physics | 2004
A. A. Soloshenko; K. V. Stepanyantz
We calculate three-loop corrections to the effective action for N=1 supersymmetric electrodynamics regularized by higher derivatives. Using the obtained results, we investigate the anomaly problem in the considered model.Three-loop quantum corrections to the effective action are calculated for N=1 supersymmetric electrodynamics, regularized by higher derivatives. Using the obtained results we investigate the anomaly puzzle in the considered model.
Physics Letters B | 2010
A. B. Pimenov; E. S. Shevtsova; K. V. Stepanyantz
It is well known that most quantum field theory models are divergent in the ultraviolet region. In order to deal with the divergent expressions, it is necessary to regularize a theory. Although physical results does not depend on regularization, a proper choice of the regularization can considerably simplify calculations or reveal some features of quantum corrections. Most calculations in the quantum field theory where made with the dimensional regularization [1]. However, the dimensional regularization is not convenient for calculations in supersymmetric theories, because it breaks the supersymmetry. That is why in supersymmetric theories one usually uses its modification, called the dimensional reduction [2]. There are a lot of calculation, made in supersymmetric theories with the dimensional reduction, see e.f. [3]. However, it is well known that the dimensional reduction is not self-consistent [4]. Ways, allowing to avoid such problems, are discussed in the literature [5]. Other regularizations are sometimes applied for calculations in supersymmetric theories. For example, in Ref. [6] two-loop β-function of the N=1 supersymmetric Yang–Mills theory was calculated with the differential renormalization [7]. A self-consistent regularization, which does not break the supersymmetry, is the higher covariant derivative regularization [8], which was generalized to the supersymmetric case in Ref. [9] (another variant was proposed in Ref. [10]). However, using this regularization is rather technically complicated. The first calculation of quantum corrections for the (non-supersymmetric) Yang–Mills theory was made in Ref. [11]. Taking into account
Nuclear Physics | 2013
A. L. Kataev; K. V. Stepanyantz
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 Z3(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.
Physics Letters B | 2014
A.L. Kataev; K. V. Stepanyantz
The exact NSVZ β-function is obtained for N = 1 SQED with Nf flavors in all orders of the perturbation theory, if the renormalization group functions are defined in terms of the bare coupling constant and the theory is regularized by higher derivatives. However, if the renormalization group functions are defined in terms of the renormalized coupling constant, the NSVZ relation between the β-function and the anomalous dimension of the matter superfields is valid only in a certain (NSVZ) scheme. We prove that forN = 1 SQED with Nf flavors the NSVZ relation is valid for the terms proportional to (Nf ) 1 in an arbitrary subtraction scheme, while the terms proportional to (Nf ) k with k ≥ 2 are scheme dependent. These results are verified by an explicit calculation of a three-loop β-function and a two-loop anomalous dimension made with the higher derivative regularization in the NSVZ and MOM subtraction schemes. In this approximation it is verified that in the MOM subtraction scheme the renormalization group functions obtained with the higher derivative regularization and with the dimensional reduction coincide.
Physics Letters B | 1997
P. I. Pronin; K. V. Stepanyantz
Abstract We explicitly calculate one-loop divergences for an arbitrary field theory model using the higher derivative regularization and nonsingular gauge condition. They are shown to agree with the results found in the dimensional regularization and do not depend on the form of regularizing term. So, the consistency of the higher derivative regularization is proven at the one-loop level. The result for the Yang-Mills theory is reproduced.We explicitly calculate one-loop divergences for an arbitrary field theory model using the higher derivative regularization and nonsingular gauge condition. They are shown to agree with the results found in the dimensional regularization and do not depend on the form of regularizing term. So, the consistency of the higher derivative regularization is proven at the one-loop level. The result for the Yang-Mills theory is reproduced.
Theoretical and Mathematical Physics | 2003
A. A. Slavnov; K. V. Stepanyantz
We propose a universal gauge-invariant renormalization scheme for supersymmetric theories. We apply this scheme to the supersymmetric quantum electrodynamics.
Theoretical and Mathematical Physics | 2014
A.L. Kataev; K. V. Stepanyantz
We briefly review the calculations of quantum corrections related with the exact NSVZ β-function in N = 1 supersymmetric theories, paying especial attention to the scheme dependence of the results. It is explained, how the NSVZ relation is obtained for the renormalization group functions defined in terms of the bare coupling constant if a theory is regularized by higher derivatives. Also we describe, how to construct a special renormalization prescription which gives the NSVZ relation for the renormalization group functions defined in terms of the renormalized coupling constant exactly in all orders for Abelian supersymmetric theories, regularized by higher derivatives. The scheme dependence of the NSVZ β-function (for the renormalization group functions defined in terms of the renormalized coupling constant) is discussed in the non-Abelian case. It is shown that in this case the NSVZ β-function leads to a certain scheme-independent equality. Dedicated to the 75-th Birthday of Prof. A.A.Slavnov
Nuclear Physics | 2014
I. L. Buchbinder; K. V. Stepanyantz
We construct a new version of the higher covariant derivative regularization for a general N = 2 supersymmetric gauge theory formulated in terms of N = 1 superfields. This regularization preserves both supersymmetries of the classical action, namely, the invariance under the manifest N = 1 supersymmetry and under the second hidden on-shell supersymmetry. The regularizing N = 2 supersymmetric higher derivative term is found in the explicit form in terms of N = 1 superfields. Thus, N = 2 supersymmetry is broken only by the gauge fixing procedure. Then we analyze the exact NSVZ β-function and prove that in the considered model its higher loop structure is determined by the anomalous dimension of the chiral superfield Φ in the adjoint representation which is the N = 2 superpartner of the gauge superfield V . Using the background field method we find that this anomalous dimension is related with the anomalous dimension of the hypermultiplet and vanishes if the effective action is invariant under N = 2 background supersymmetry. As a consequence, in this case the higher loop contributions to β-function also vanish. The one-loop renormalization structure in the considered regularization is also studied by the explicit calculations of the one-loop renormalization constants.
Theoretical and Mathematical Physics | 2004
A. A. Slavnov; K. V. Stepanyantz
A manifestly invariant renormalization scheme of N=1 nonabelian supersymmetric gauge theories is proposed.
Physics Letters B | 2015
I. L. Buchbinder; N.G. Pletnev; K. V. Stepanyantz
We formulate the higher covariant derivative regularization for N = 2 supersymmetric gauge theories in N = 2 harmonic superspace. This regularization is constructed by adding the N = 2 supersymmetric higher derivative term to the classical action and inserting the N = 2 supersymmetric Pauli–Villars determinants into the generating functional for removing one-loop divergencies. Unlike all other regularization schemes in N = 2 supersymmetric quantum field theory, this regularization preserves by construction the manifest N = 2 supersymmetry at all steps of calculating loop corrections to the effective action. Together with N = 2 supersymmetric background field method this regularization allows to calculate quantum corrections without breaking the manifest gauge symmetry and N = 2 supersymmetry. Thus, we justify the assumption about existence of a regularization preserving N = 2 supersymmetry, which is a key element of the N = 2 non-renormalization theorem. As a result, we give the prove of the N = 2 non-renormalization theorem which does not require any additional assumptions.