Searcharxiv⌕ Search

arXiv subjects

K. V. Stepanyantz

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

At least 55 records · Page 3Linked to original sources
arXiv2015

Manifestly N=2 supersymmetric regularization for N=2 supersymmetric field theories

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.

hep-th↗
arXiv2015

Derivation of the exact expression for the D function in N=1 SQCD

We discuss various details of our derivation of the exact expression for the Adler D function in N=1 supersymmetric QCD (SQCD). This exact formula relates the D function to anomalous dimensions of the matter superfields. Our perturbative derivation refers to the D function defined in terms of the bare coupling constant in the case of using the higher covariant derivative regularization. The exact expression for this function is obtained by direct summation of supergraphs to all orders in the non-Abelian coupling constant. As we argued previously, our formula should be valid beyond perturbation theory too. The perturbative result we present here coincides with the general formula order by order. We discuss consequences for N=1 SQCD in the conformal window. It is noted that our exact relation can allow one to determine the (infrared) critical anomalous dimension of the Seiberg M field present in the dual theory.

hep-th↗
arXiv2014

Relation between two-point Green functions of ${\cal N}=1$ SQED with $N_f$ flavors, regularized by higher derivatives, in the three-loop approximation

We verify the identity which relates the two-point Green functions of ${\cal N}=1$ SQED with $N_f$ flavors, regularized by higher derivatives, by explicit calculations in the three-loop approximation. This identity explains why in the limit of the vanishing external momentum the two-point Green function of the gauge superfield is given by integrals of double total derivatives in the momentum space. It also allows to derive the NSVZ $β$-function exactly in all loops if the renormalization group functions are defined in terms of the bare coupling constant. In order to verify the considered identity we use it for constructing integrals giving the three-loop $β$-function starting from the two-point Green functions of the matter superfields in the two-loop approximation. Then we demonstrate that the results for these integrals coincide with the sums of the corresponding three-loop supergraphs.

hep-th↗
arXiv2014

The NSVZ beta-function and the Schwinger-Dyson equations for N=1 SQED with N_f flavors, regularized by higher derivatives

The effective diagram technique based on the Schwinger-Dyson equations is constructed for N=1 SQED with N_f flavors, regularized by higher derivatives. Using these effective diagrams, it is possible to derive the exact NSVZ relation between the beta-function and the anomalous dimension of the matter superfields exactly in all loops, if the renormalization group functions are defined in terms of the bare coupling constant. In particular, we verify that all integrals which give the beta-function defined in terms of the bare coupling constant are integrals of double total derivatives and prove some identities relating Green functions.

hep-th↗
arXiv2014

The NSVZ beta-function in supersymmetric theories with different regularizations and renormalization prescriptions

We briefly review the calculations of quantum corrections related with the exact NSVZ $β$-function in ${\cal N}=1$ 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.

hep-th↗
arXiv2014

The higher derivative regularization and quantum corrections in ${\cal N}=2$ supersymmetric theories

We construct a new version of the higher covariant derivative regularization for a general ${\cal N}=2$ supersymmetric gauge theory formulated in terms of ${\cal N}=1$ superfields. This regularization preserves both supersymmetries of the classical action, namely, the invariance under the manifest ${\cal N}=1$ supersymmetry and under the second hidden on-shell supersymmetry. The regularizing ${\cal N}=2$ supersymmetric higher derivative term is found in the explicit form in terms of ${\cal N}=1$ superfields. Thus, ${\cal N}=2$ 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 ${\cal N}=2$ 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 ${\cal N}=2$ 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.

hep-th↗
arXiv2014

Scheme independent consequence of the NSVZ relation for N=1 SQED with N_f flavors

The exact NSVZ $β$-function is obtained for ${\cal N}=1$ SQED with $N_f$ 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 for ${\cal N}=1$ SQED with $N_f$ flavors the NSVZ relation is valid for the terms proportional to $(N_f)^1$ in an arbitrary subtraction scheme, while the terms proportional to $(N_f)^k$ with $k\ge 2$ 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.

hep-th↗
arXiv2013

NSVZ scheme with the higher derivative regularization for N=1 SQED

The exact NSVZ relation between a $β$-function of ${\cal N}=1$ 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 ${\cal N}=1$ 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 $\bar{DR}$ scheme and the NSVZ scheme defined within the higher derivative approach by the finite renormalization.

hep-th↗
arXiv2012

Multiloop calculations in supersymmetric theories with the higher covariant derivative regularization

Most calculations of quantum corrections in supersymmetric theories are made with the dimensional reduction, which is a modification of the dimensional regularization. However, it is well known that the dimensional reduction is not self-consistent. A consistent regularization, which does not break the supersymmetry, is the higher covariant derivative regularization. However, the integrals obtained with this regularization can not be usually calculated analytically. We discuss application of this regularization to the calculations in supersymmetric theories. In particular, it is demonstrated that integrals defining the beta-function are possibly integrals of total derivatives. This feature allows to explain the origin of the exact NSVZ beta-function, relating the beta-function with the anomalous dimensions of the matter superfields. However, integrals for the anomalous dimension should be calculated numerically.

hep-th↗
arXiv2011

Factorization of integrals defining the two-loop beta-function for the general renormalizable N=1 SYM theory, regularized by the higher covariant derivatives, into integrals of double total derivatives

The integrals defining the two-loop beta-function for the general renormalizable N=1 supersymmetric Yang--Mills theory, regularized by higher covariant derivatives, are investigated. It is shown that they are given by integrals of double total derivatives. These integrals are not equal to zero due to appearing of delta-functions. These delta-functions allow to reduce the two-loop integrals to one-loop integrals, which can be easily calculated. The result agrees with the exact NSVZ beta-function and calculations made by different methods.

hep-th↗
arXiv2011

Derivation of the exact NSVZ beta-function in N=1 SQED, regularized by higher derivatives, by direct summation of Feynman diagrams

For N=1 supersymmetric quantum electrodynamics, regularized by higher derivatives, a method for summation of all Feynman diagrams defining the beta-function is presented. Using this method we prove that the beta-function is given by an integral of a total derivative, which can be easily calculated. It is shown that surviving terms give the exact NSVZ beta-function. The results are compared with the explicit three-loop calculation.

hep-th↗
arXiv2007

Higher derivative regularization and quantum corrections in N=1 supersymmetric theories

We review some results of applying the higher covariant derivative regularization to the investigation of quantum corrections structure in N=1 supersymmetric theories. In particular, we demonstrate that all integrals, defining the Gell-Mann--Low function in supersymmetric theories, are integrals of total derivatives. As a consequence, there is an identity for Green functions, which does not follow from any known symmetry of the theory, in N=1 supersymmetric theories. We also discuss how to derive the exact $β$-function by methods of the perturbation theory.

hep-th↗
arXiv2007

Verification of new identity for the Green functions in N=1 supersymmetric non-Abelian Yang--Mills theory with the matter fields

We investigate a new identity for Green functions using the higher covariant derivative regularization. It relates some coefficients in the vertex function of the matter superfield, in which one of external matter lines is not chiral. The calculation in the first nontrivial order (for the two-loop vertex function) reveals that the new identity is also valid for the non-Abelian Yang--Mills theory with matter fields. The new identity is shown to appear because three-loop integrals, defining the Gell-Mann--Low function are factorized into integrals of total derivatives.

hep-th↗
arXiv2006

Contribution of matter fields to the Gell-Mann-Low function for N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives

Contribution of matter fields to the Gell-Mann-Low function for N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives, is obtained using Schwinger-Dyson equations and Slavnov-Tailor identities. A possible deviation of the result from the corresponding contribution in the exact Novikov, Shifman, Vainshtein and Zakharov $β$-function is discussed.

hep-th↗