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K. V. Stepanyantz

Publications and source records attributed to K. V. Stepanyantz.

At least 37 records · Page 2Linked to original sources
arXiv2018

Two-loop renormalization of the Faddeev--Popov ghosts in ${\cal N}=1$ supersymmetric gauge theories regularized by higher derivatives

For the general renormalizable ${\cal N}=1$ supersymmetric gauge theory we investigate renormalization of the Faddeev--Popov ghosts using the higher covariant derivative regularization. First, we find the two-loop anomalous dimension defined in terms of the bare coupling constant in the general $ξ$-gauge. It is demonstrated that for doing this calculation one should take into account that the quantum gauge superfield is renormalized in a nonlinear way. Next, we obtain the two-loop anomalous dimension of the Faddeev--Popov ghosts defined in terms of the renormalized coupling constant and examine its dependence on the subtraction scheme.

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arXiv2018

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

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 ${\cal N}=1$ 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 $\lnΛ/μ$ are included into the renormalization constants.

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arXiv2017

On the two-loop divergences of the 2-point hypermultiplet supergraphs for $6D$, ${\cal N} = (1,1)$ SYM theory

We consider $6D$, ${\cal N}=(1,1)$ supersymmetric Yang-Mills theory formulated in ${\cal N}=(1,0)$ harmonic superspace and analyze the structure of the two-loop divergences in the hypermultiplet sector. Using the ${\cal N}=(1,0)$ superfield background field method we study the two-point supergraphs with the hypermultiplet legs and prove that their total contribution to the divergent part of effective action vanishes off shell.

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arXiv2017

New form of the NSVZ relation at the two-loop level

Recently the exact NSVZ $β$-function was rewritten in the form of a relation between the $β$-function and the anomalous dimensions of the quantum gauge superfield, of the Faddeev--Popov ghosts, and of the matter superfields. It was also suggested that this form of the NSVZ equation follows from an underlying equation relating two-point Green functions of the theory. Here we demonstrate that this relation is satisfied at the two-loop level for the non-Abelian ${\cal N}=1$ supersymmetric gauge theories in the case of using the simplest (BRST non-invariant) version of the higher covariant derivative regularization. Consequently, the integrals giving the two-loop $β$-function can be reduced to the one-loop integrals giving the anomalous dimensions of the quantum gauge superfield, of the Faddeev--Popov ghosts, and of the matter superfields.

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arXiv2017

Structure of quantum corrections in ${\cal N}=1$ supersymmetric gauge theories

Some recent research of quantum corrections in ${\cal N}=1$ supersymmetric theories is briefly reviewed. The most attention is paid to the theories regularized by higher covariant derivatives. In particular, we discuss, how the NSVZ and NSVZ-like relations appear with this regularization and how one can construct the NSVZ scheme in all orders.

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arXiv2017

The Adler $D$-function for ${\cal N}=1$ SQCD regularized by higher covariant derivatives in the three-loop approximation

We calculate the Adler $D$-function for ${\cal N}=1$ SQCD in the three-loop approximation using the higher covariant derivative regularization and the NSVZ-like subtraction scheme. The recently formulated all-order relation between the Adler function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant is first considered and generalized to the case of an arbitrary representation for the chiral matter superfields. The correctness of this all-order relation is explicitly verified at the three-loop level. The special renormalization scheme in which this all-order relation remains valid for the $D$-function and the anomalous dimension defined in terms of the renormalized coupling constant is constructed in the case of using the higher derivative regularization. The analytic expression for the Adler function for ${\cal N}=1$ SQCD is found in this scheme to the order $O(α_s^2)$. The problem of scheme-dependence of the $D$-function and the NSVZ-like equation is briefly discussed.

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arXiv2017

One-loop polarization operator of the quantum gauge superfield for ${\cal N}=1$ SYM regularized by higher derivatives

We consider the general ${\cal N}=1$ supersymmetric gauge theory with matter, regularized by higher covariant derivatives without breaking the BRST invariance, in the massless limit. In the $ξ$-gauge we obtain the (unrenormalized) expression for the two-point Green function of the quantum gauge superfield in the one-loop approximation as a sum of integrals over the loop momentum. The result is presented as a sum of three parts: the first one corresponds to the pure supersymmetric Yang--Mills theory in the Feynman gauge, the second one contains all gauge dependent terms, and the third one is the contribution of diagrams with a matter loop. For the Feynman gauge and a special choice of the higher derivative regulator in the gauge fixing term we analytically calculate these integrals in the limit $k\to 0$. In particular, in addition to the leading logarithmically divergent terms, which are determined by integrals of double total derivatives, we also find the finite constants.

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arXiv2017

Supergraph analysis of the one-loop divergences in $6D$, ${\cal N} = (1,0)$ and ${\cal N} = (1,1)$ gauge theories

We study the one-loop effective action for $6D,$ ${\cal N}=(1,0)$ supersymmetric Yang--Mills (SYM) theory with hypermultiplets and $6D,$ ${\cal N}=(1,1)$ SYM theory as a subclass of the former, using the off-shell formulation of these theories in $6D,$ ${\cal N}=(1,0)$ harmonic superspace. We develop the corresponding supergraph technique and apply it to compute the one-loop divergences in the background field method ensuring the manifest gauge invariance. We calculate the two-point Green functions of the gauge superfield and the hypermultiplet, as well as the three-point gauge-hypermultipet Green function. Using these Green functions and exploiting gauge invariance of the theory, we find the full set of the off-shell one-loop divergent contributions, including the logarithmic and power ones. Our results precisely match with those obtained earlier in [1,2] within the proper time superfield method.

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arXiv2017

Exact renormalization of the photino mass in softly broken ${\cal N}=1$ SQED with $N_f$ flavors regularized by higher derivatives

We consider the softly broken ${\cal N}=1$ supersymmetric electrodynamics, regularized by higher derivatives. For this theory we demonstrate that the renormalization of the photino mass is determined by integrals of double total derivatives in the momentum space in all orders. Consequently, it is possible to derive the NSVZ-like exact relation between the photino mass anomalous dimension and the anomalous dimension of the matter superfields in the rigid theory by direct summation of supergraphs. It is important that both these renormalization group functions are defined in terms of the bare coupling constant, so that the considered NSVZ-like relation is valid independently of the subtraction scheme in the case of using the higher derivative regularization. The factorization of integrals defining the photino mass renormalization into integrals of double total derivatives is verified by an explicit two-loop calculation.

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arXiv2017

Three-loop NSVZ relation for terms quartic in the Yukawa couplings with the higher covariant derivative regularization

We demonstrate that in non-Abelian ${\cal N}=1$ supersymmetric gauge theories the NSVZ relation is valid for terms quartic in the Yukawa couplings independently of the subtraction scheme if the renormalization group functions are defined in terms of the bare couplings and the theory is regularized by higher covariant derivatives. The terms quartic in the Yukawa couplings appear in the three-loop $β$-function and in the two-loop anomalous dimension of the matter superfields. We have obtained that the three-loop contribution to the $β$-function quartic in the Yukawa couplings is given by an integral of double total derivatives. Consequently, one of the loop integrals can be taken and the three-loop contribution to the $β$-function is reduced to the two-loop contribution to the anomalous dimension. The remaining loop integrals have been calculated for the simplest form of the higher derivative regularizing term. Then we construct the renormalization group functions defined in terms of the renormalized couplings. In the considered approximation they do not satisfy the NSVZ relation for a general renormalization prescription. However, we verify that the recently proposed boundary conditions defining the NSVZ scheme in the non-Abelian case really lead to the NSVZ relation between the terms of the considered structure.

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arXiv2017

One-loop divergences in 6D, N=(1,0) SYM theory

We consider, in the harmonic superspace approach, the six-dimensional N=(1,0) supersymmetric Yang-Mills gauge multiplet minimally coupled to a hypermultiplet in an arbitrary representation of the gauge group. Using the superfield proper-time and background-field techniques, we compute the divergent part of the one-loop effective action depending on both the gauge multiplet and the hypermultiplet. We demonstrate that in the particular case of N=(1,1) SYM theory, which corresponds to the hypermultiplet in the adjoint representation, all one-loop divergencies vanish, so that N=(1,1) SYM theory is one-loop finite {\it off shell}.

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arXiv2016

NSVZ-like scheme for the photino mass in softly broken ${\cal N}=1$ SQED regularized by higher derivatives

In the case of using the higher derivative regularization we construct the subtraction scheme which gives the NSVZ-like relation for the anomalous dimension of the photino mass in softly broken ${\cal N}=1$ SQED with $N_f$ flavors in all loops. The corresponding renormalization prescription is determined by simple boundary conditions imposed on the renormalization constants. It allows fixing an arbitrariness of choosing finite counterterms in every order of the perturbation theory in such a way that the renormalization group functions defined in terms of the renormalized coupling constant satisfy the NSVZ-like relation.

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arXiv2016

One-loop divergences in the 6D, N=(1,0) abelian gauge theory

We consider, in the harmonic superspace approach, the six-dimensional N=(1,0) supersymmetric model of abelian gauge multiplet coupled to a hypermultiplet. The superficial degree of divergence is evaluated and the structure of possible one-loop divergences is analyzed. Using the superfield proper-time and background-field technique, we compute the divergent part of the one-loop effective action depending on both the gauge multiplet and the hypermultiplet. The corresponding counterterms contain the purely gauge multiplet contribution together with the mixed contributions of the gauge multiplet and hypermultiplet. We show that the theory is on-shell one-loop finite in the gauge multiplet sector in agreement with the results of [1]. The divergences in the mixed sector cannot be eliminated by any field redefinition, implying the theory to be UV divergent at one loop.

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arXiv2016

The NSVZ scheme for ${\cal N}=1$ SQED with $N_f$ flavors, regularized by the dimensional reduction, in the three-loop approximation

At the three-loop level we analyze, how the NSVZ relation appears for ${\cal N}=1$ SQED regularized by the dimensional reduction. This is done by the method analogous to the one which was earlier used for the theories regularized by higher derivatives. Within the dimensional technique, the loop integrals cannot be written as integrals of double total derivatives. However, similar structures can be written in the considered approximation and are taken as a starting point. Then we demonstrate that, unlike the higher derivative regularization, the NSVZ relation is not valid for the renormalization group functions defined in terms of the bare coupling constant. However, for the renormalization group functions defined in terms of the renormalized coupling constant, it is possible to impose boundary conditions to the renormalization constants giving the NSVZ scheme in the three-loop order. They are similar to the all-loop ones defining the NSVZ scheme obtained with the higher derivative regularization, but are more complicated. The NSVZ schemes constructed with the dimensional reduction and with the higher derivative regularization are related by a finite renormalization in the considered approximation.

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arXiv2016

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

We consider a general non-Abelian renormalizable ${\cal N}=1$ 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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arXiv2015

Equation for one-loop divergences in two dimensions and its application to higher spin fields

A simple formula for one-loop logarithmic divergences on the background of a two-dimensional curved space-time is derived for theories for which the second variation of the action is a nonminimal second order operator with small nonminimal terms. In particular, this formula allows to calculate terms which are integrals of total derivatives. As an application of the result, one-loop divergences for the higher spin fields on the constant curvature background are obtained in a nonminimal gauge, which depends on two parameters. By an explicit calculation we demonstrate that with the considered accuracy the result is gauge independent. Moreover, the result appeared to be independent of the spin $s$ for $s\ge 3$.

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arXiv2015

Structure of three-loop contributions to the beta-function of N=1 SQED with N_f flavors, regularized by the dimensional reduction

In the case of using the higher derivative regularization for $N=1$ SQED with $N_f$ flavors the loop integrals giving the $β$-function are integrals of double total derivatives in the momentum space. This feature allows to reduce one of the loop integrals to an integral of the $δ$-function and to derive the NSVZ relation for the renormalization group functions defined in terms of the bare coupling constant. In this paper we consider $N=1$ SQED with $N_f$ flavors regularized by the dimensional reduction in the $\overline{\mbox{DR}}$-scheme. Evaluating the scheme-dependent three-loop contribution to the $β$-function proportional to $(N_f)^2$ we find the structures analogous to integrals of the $δ$-singularities. After adding the scheme-independent terms proportional to $(N_f)^1$ we obtain the known result for the three-loop $β$-function.

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