# K. V. Stepanyantz's research while affiliated with Moscow State Textile University and other places

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## Publications (145)

We demonstrate that in the $P=\frac{1}{3}Q$ supersymmetric theories the renormalization group invariance of the ratio $\lambda^{ijk}/e$ (of the Yukawa couplings to the gauge coupling) is equivalent to a simple relation between the anomalous dimensions of the quantum gauge superfield, of the Faddeev--Popov ghosts, and of the matter superfields, whic...

A bstract
We study the off-shell structure of the two-loop effective action in 6 D, $$ \mathcal{N} $$ N = (1 , 1) supersymmetric gauge theories formulated in $$ \mathcal{N} $$ N = (1 , 0) harmonic superspace. The off-shell effective action involving all fields of 6 D, $$ \mathcal{N} $$ N = (1 , 1) supermultiplet is constructed by the harmonic super...

We analyze quantum properties of N=2 and N=4 supersymmetric gauge theories formulated in terms of N=1 superfields and investigate the conditions imposed on a renormalization prescription under which the nonrenormalization theorems are valid. For this purpose in these models we calculate the two-loop contributions to the anomalous dimensions of all...

The gauge coupling unification is investigated at the classical level under the assumptions that the gauge symmetry breaking chain is $E_8\to E_7\times U_1 \to E_6\times U_1 \to SO_{10}\times U_1 \to SU_5 \times U_1 \to SU_3 \times SU_2 \times U_1$ and only components of the representations 248 of $E_8$ can acquire vacuum expectation values. We dem...

We analyse quantum properties of ${\cal N}=2$ and ${\cal N}=4$ supersymmetric gauge theories formulated in terms of ${\cal N}=1$ superfields and investigate the conditions imposed on a renormalization prescription under which the non-renormalization theorems are valid. For this purpose in these models we calculate the two-loop contributions to the...

We study the off-shell structure of the two-loop effective action in $6D, {\cal N}=(1,1)$ supersymmetric gauge theories formulated in ${\cal N}=(1,0)$ harmonic superspace. The off-shell effective action involving all fields of $6D, {\cal N}=(1,1)$ supermultiplet is constructed by the harmonic superfield background field method, which ensures both m...

For renormalizable theories with a single coupling constant regularized by higher derivatives we investigate the coefficients at powers of logarithms present in the renormalization constants assuming that divergences are removed by minimal subtractions of logarithms. According to this higher-derivatives and minimal-subtractions-of-logarithms (HD+MS...

A bstract
Three-loop β -functions of the Minimal Supersymmetric Standard Model regularized by higher covariant derivatives are obtained for an arbitrary supersymmetric subtraction scheme. For this purpose we first calculate two-loop anomalous dimensions for all MSSM chiral matter superfields defined in terms of the bare couplings. Then we use the N...

For renormalizable theories with a single coupling constant regularized by higher derivatives we investigate the coefficients at powers of logarithms present in the renormalization constants assuming that divergences are removed by minimal subtractions of logarithms. According to this (HD+MSL) renormalization prescription the renormalization consta...

Three-loop $\beta$-functions of the Minimal Supersymmetric Standard Model regularized by higher covariant derivatives are obtained for an arbitrary supersymmetric subtraction scheme. For this purpose we first calculate two-loop anomalous dimensions for all MSSM chiral matter superfields defined in terms of the bare couplings. Then we use the NSVZ e...

A bstract
For $$ \mathcal{N} $$ N = 1 SQED with N f flavors regularized by higher derivatives in the general ξ -gauge we calculate the three-loop anomalous dimension of the matter superfields defined in terms of the bare coupling constant and demonstrate its gauge independence. After this the four-loop β -function defined in terms of the bare coupl...

In this paper, we verify a method which allows to obtain the [Formula: see text]-function of supersymmetric theories regularized by higher covariant derivatives by calculating only specially modified vacuum supergraphs. With the help of this method for a general renormalizable [Formula: see text] supersymmetric gauge theory, a part of the three-loo...

For ${\cal N}=1$ SQED with $N_f$ flavors regularized by higher derivatives in the general $\xi$-gauge we calculate the three-loop anomalous dimension of the matter superfields defined in terms of the bare coupling constant and demonstrate its gauge independence. After this the four-loop $\beta$-function defined in terms of the bare coupling constan...

By an explicit calculation we demonstrate that the triple gauge-ghost vertices in a general renormalizable $${{\mathcal {N}}}=1$$ N = 1 supersymmetric gauge theory are UV finite in the two-loop approximation. For this purpose we calculate the two-loop divergent contribution to the $$\bar{c}^+ V c$$ c ¯ + V c -vertex proportional to $$(C_2)^2$$ ( C...

We verify a method which allows to obtain the $\beta$-function of supersymmetric theories regularized by higher covariant derivatives by calculating only specially modified vacuum supergraphs. With the help of this method for a general renormalizable ${\cal N}=1$ supersymmetric gauge theory a part of the three-loop $\beta$-function depending on the...

Structure of quantum corrections in ${\cal N}=1$ supersymmetric gauge theories is investigated in the case of using the regularization by higher covariant derivatives. It is demonstrated that this regularization allows revealing some interesting features which lead to the exact relations between the renormalization group functions. In particular, t...

By an explicit calculation we demonstrate that the triple gauge-ghost vertices in a general renormalizable ${\cal N}=1$ supersymmetric gauge theory are UV finite in the two-loop approximation. For this purpose we calculate the two-loop divergent contribution to the $\bar c^+ V c$-vertex proportional to $(C_2)^2$ and use the finiteness of the two-lo...

A bstract
We investigate the NSVZ relations for $$ \mathcal{N} $$ N = 1 supersymmetric gauge theories with multiple gauge couplings. As examples, we consider MSSM and the flipped SU(5) model, for which they easily reproduce the results for the two-loop β -functions. For $$ \mathcal{N} $$ N = 1 SQCD interacting with the Abelian gauge superfield we d...

We investigate the NSVZ relations for ${\cal N}=1$ supersymmetric gauge theories with multiple gauge couplings. As examples, we consider MSSM and the flipped $SU(5)$ model, for which they easily reproduce the results for the two-loop $\beta$-functions. For ${\cal N}=1$ SQCD interacting with the Abelian gauge superfield we demonstrate that the NSVZ-...

For a general renormalizable N=1 supersymmetric gauge theory with a simple gauge group we verify the ultraviolet (UV) finiteness of the two-loop matter contribution to the triple gauge-ghost vertices. These vertices have one leg of the quantum gauge superfield and two legs corresponding to the Faddeev–Popov ghost and antighost. By an explicit calcu...

We continue studying 6D,N=(1,1) supersymmetric Yang-Mills (SYM) theory in the N=(1,0) harmonic superspace formulation. Using the superfield background field method we explore the two-loop divergences of the effective action in the gauge multiplet sector. It is explicitly demonstrated that among four two-loop background-field dependent supergraphs c...

We consider a one-loop finite $$\mathcal{N}=1$$ N = 1 supersymmetric theory in such a renormalization scheme that the first L contributions to the gauge $$\beta $$ β -function and the first $$(L-1)$$ ( L - 1 ) contributions to the anomalous dimension of the matter superfields and to the Yukawa $$\beta $$ β -function vanish. It is demonstrated that...

We consider a one-loop finite ${\cal N}=1$ supersymmetric theory in such a renormalization scheme that the first $L$ contributions to the gauge $\beta$-function and the first $(L-1)$ contributions to the anomalous dimension of the matter superfields and to the Yukawa $\beta$-function vanish. It is demonstrated that in this case the NSVZ equation an...

We continue studying $6D, {\cal N}=(1,1)$ supersymmetric Yang-Mills (SYM) theory in the ${\cal N}=(1,0)$ harmonic superspace formulation. Using the superfield background field method we explore the two-loop divergencies of the effective action in the gauge multiplet sector. It is explicitly demonstrated that among four two-loop background-field dep...

For a general renormalizable ${\cal N}=1$ supersymmetric gauge theory with a simple gauge group we verify the ultraviolet (UV) finiteness of the two-loop matter contribution to the triple gauge-ghost vertices. These vertices have one leg of the quantum gauge superfield and two legs corresponding to the Faddeev--Popov ghost and antighost. By an expl...

We consider the harmonic superspace formulation of higher-derivative 6D,N=(1,0) supersymmetric gauge theory and its minimal coupling to a hypermultiplet. In components, the kinetic term for the gauge field in such a theory involves four space-time derivatives. The theory is quantized in the framework of the superfield background method ensuring man...

The perturbative all-loop derivation of the NSVZ β-function for N=1 supersymmetric gauge theories regularized by higher covariant derivatives is finalized by calculating the sum of singularities produced by quantum superfields. These singularities originate from integrals of double total derivatives and determine all contributions to the β-function...

A bstract
We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6 D , $$ \mathcal{N} $$ N = (1 , 0) supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis...

The perturbative all-loop derivation of the NSVZ $\beta$-function for ${\cal N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives is finalized by calculating the sum of singularities produced by quantum superfields. These singularities originate from integrals of double total derivatives and determine all contributions to...

We consider the harmonic superspace formulation of higher-derivative $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory and its minimal coupling to a hypermultiplet. In components, the kinetic term for the gauge field in such a theory involves four space-time derivatives.The theory is quantized in the framework of the superfield background method e...

The two-loop anomalous dimension of the chiral matter superfields is calculated for a general \( \mathcal{N} \) = 1 supersymmetric gauge theory regularized by higher covariant derivatives. We obtain both the anomalous dimension defined in terms of the bare couplings, and the one defined in terms of the renormalized couplings for an arbitrary renorm...

We discuss why the Slavnov higher covariant derivative regularization appeared to be an excellent instrument for investigating quantum corrections in supersymmetric gauge theories. For example, it allows demonstrating that the β-function in these theories is given by integrals of double total derivatives and to construct the Novikov-Shifman-Vainsht...

We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of $6D$, ${\cal N}=(1,0)$ supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifest...

We verify a recently proposed method for obtaining a β-function of N=1 supersymmetric gauge theories regularized by higher derivatives by an explicit calculation. According to this method, a β-function can be found by calculating specially modified vacuum supergraphs instead of a much larger number of the two-point superdiagrams. The result is prod...

The two-loop anomalous dimension of the chiral matter superfields is calculated for a general ${\cal N}=1$ supersymmetric gauge theory regularized by higher covariant derivatives. We obtain both the anomalous dimension defined in terms of the bare couplings, and the one defined in terms of the renormalized couplings for an arbitrary renormalization...

We verify a recently proposed method for obtaining a $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories regularized by higher derivatives by an explicit calculation. According to this method, a $\beta$-function can be found by calculating specially modified vacuum supergraphs instead of a much larger number of the two-point superdiagram...

The three-loop Adler $D$-function for ${\cal N}=1$ SQCD in the $\overline{\mbox{DR}}$ scheme is calculated. It appears that the result does not satisfy NSVZ-like equation which relates the $D$-function to the anomalous dimension of the matter superfields. However this NSVZ-like equation can be restored by a special tuning of the renormalization sch...

The contributions of the matter superfields and of the Faddeev-Popov ghosts to the β-function of \( \mathcal{N} \) = 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...

The contributions of the matter superfields and of the Faddeev--Popov ghosts to the $\beta$-function of ${\cal N}=1$ 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 $\b...

We discuss, how the exact NSVZ -function appears in N = 1 supersymmetric non-Abelian gauge theories, regularized by higher covariant derivatives. In particular, we demonstrate that the renormalization group functions defined in terms of the bare couplings satisfy the NSVZ relation in the case of using this regularization. This occurs, because the l...

We discuss why the Slavnov higher covariant derivative regularization appeared to be an excellent instrument for investigating quantum corrections in supersymmetric gauge theories. For example, it allowed to demonstrate that the $\beta$-function in these theories is given by integrals of double total derivatives and to construct the NSVZ renormaliz...

A bstract
For a general $$ \mathcal{N} $$ N = 1 supersymmetric gauge theory regularized by higher covariant derivatives we prove in all orders that the β -function defined in terms of the bare couplings is given by integrals of double total derivatives with respect to loop momenta. With the help of the technique used for this proof it is possible t...

We study the gauge dependence of one-loop divergences in a general matter-coupled 6D, N=(1,0) supersymmetric gauge theory in the harmonic superspace formulation. Our analysis is based on the effective action constructed by the background superfield method, with the gauge-fixing term involving one real parameter ξ0. A manifestly gauge invariant and...

We find the three-loop contribution to the \(\beta \)-function of \(\mathcal{N}=1\) supersymmetric gauge theories regularized by higher covariant derivatives produced by the supergraphs containing loops of the Faddeev–Popov ghosts. This is done using a recently proposed algorithm, which essentially simplifies such multiloop calculations. The result...

We find the three-loop contribution to the $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives produced by the supergraphs containing loops of the Faddeev--Popov ghosts. This is done using a recently proposed algorithm, which essentially simplifies such multiloop calculations. The result is pre...

For a general ${\cal N}=1$ supersymmetric gauge theory regularized by higher covariant derivatives we prove in all orders that the $\beta$-function defined in terms of the bare couplings is given by integrals of double total derivatives with respect to loop momenta. With the help of the technique used for this proof it is possible to construct a me...

We study the gauge dependence of one-loop divergences in a general matter-coupled $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory in the harmonic superspace formulation. Our analysis is based on the effective action constructed by the background superfield method, with the gauge-fixing term involving one real parameter $\xi_0$. A manifestly gaug...

In this paper we investigate the renormalization of N=1 supersymmetric quantum electrodynamics, regularized by higher derivatives, in the on-shell scheme. It is demonstrated that in this scheme the exact Novikov, Shifman, Vainshtein, and Zakharov (NSVZ) equation relating the β-function to the anomalous dimension of the matter superfields is valid i...

In this paper we investigate the renormalization of ${\cal N}=1$ supersymmetric quantum electrodynamics, regularized by higher derivatives, in the on-shell scheme. It is demonstrated that in this scheme the exact Novikov, Shifman, Vainshtein, and Zakharov (NSVZ) equation relating the $\beta$-function to the anomalous dimension of the matter superfi...

A bstract
The three-loop Adler D -function for $$ \mathcal{N}=1 $$ N = 1 SQCD in the $$ \overline{\mathrm{DR}} $$ D R ¯ scheme is calculated starting from the three-loop result recently obtained with the higher covariant derivative regularization. For this purpose, for the theory regularized by higher derivatives we find a subtraction scheme in whi...

The three-loop Adler $D$-function for ${\cal N}=1$ SQCD in the $\overline{\mbox{DR}}$ scheme is calculated starting from the three-loop result recently obtained with the higher covariant derivative regularization. For this purpose, for the theory regularized by higher derivatives we find a subtraction scheme in which the Green functions coincide wi...

We review the recent progress in studying the quantum structure of 6 D , N = ( 1 , 0 ) , and N = ( 1 , 1 ) supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly N = ( 1 , 0 ) supersymme...

We review the recent progress in studying the quantum structure of $6D$, ${\cal N}=(1,0)$ and ${\cal N}=(1,1)$ supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly ${\cal N}=(1,0)$ sup...

We study the gauge dependence of the one-loop effective action for the abelian 6D, N=(1,0) supersymmetric gauge theory formulated in harmonic superspace. We introduce the superfield ξ-gauge, construct the corresponding gauge superfield propagator, and calculate the one-loop two- and three-point Green functions with two external hypermultiplet legs....

We investigate the NSVZ equation in N = 1 supersymmetric gauge theories, which relates the β-function to the anomalous dimension of the matter superfields. In particular, we argue that it is closely connected with the non-renormalization theorem for the three-point gauge-ghost vertices (in which one external leg corresponds to the quantum gauge sup...

For the N=1 supersymmetric electrodynamics we investigate renormalization schemes in which the NSVZ equation relating the β-function to the anomalous dimension of the matter superfields is valid in all loops. We demonstrate that there is an infinite set of such schemes. They are related by finite renormalizations which form a group and are paramete...

We study the gauge dependence of the one-loop effective action for the abelian $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory formulated in harmonic superspace. We introduce the superfield $\xi$-gauge, construct the corresponding gauge superfield propagator, and calculate the one-loop two-and three-point Green functions with two external hyperm...

For the ${\cal N}=1$ supersymmetric electrodynamics we investigate renormalization schemes in which the NSVZ equation relating the $\beta$-function to the anomalous dimension of the matter superfields is valid in all loops. We demonstrate that there is an infinite set of such schemes. They are related by finite renormalizations which form a group a...

A bstract
For the general renormalizable $$ \mathcal{N}=1 $$ 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 tha...

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 $\xi$-gauge. It is demonstrated that for doing this ca...

The paper contains analysis of the one-loop effective action for affine-metric gravity of the Hilbert-Einstein type with the cosmological term. We discuss different approaches to the calculation of the effective action, which depends on two independent variables, namely, the metric tensor and the affine connection. In the one-loop approximation we...

A bstract
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 $$ \mathcal{N} $$ N = 1 supersymmetric gauge theory, regularized by...

We investigate quantum corrections in = 1 non-Abelian supersymmetric gauge theories, regularized by higher covariant derivatives. In particular, by the help of the Slavnov–Taylor identities we prove that the vertices with two ghost legs and one leg of the quantum gauge superfield are finite in all orders. This non-renormalization theorem is confirm...

We investigate the structure of quantum corrections in N = 1 supersymmetric theories using the higher covariant derivative method for regularization. In particular, we discuss the non-renormalization theorem for the triple gauge-ghost vertices and its connection with the exact NSVZ β-function. Namely, using the finiteness of the triple gauge-ghost...

We calculate the three-loop Adler $D$-function of ${\cal N}=1$ SQCD regularized by higher covariant derivatives and find the subtraction scheme in which the exact NSVZ-like relation for this function that was recently proposed is valid.

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...

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.

Recently the exact NSVZ $\beta$-function was rewritten in the form of a relation between the $\beta$-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 Gree...

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 constan...

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 $\xi$-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...

We study the one-loop effective action for 6D,N=(1,0) supersymmetric Yang–Mills (SYM) theory with hypermultiplets and 6D,N=(1,1) SYM theory as a subclass of the former, using the off-shell formulation of these theories in 6D,N=(1,0) harmonic superspace. We develop the corresponding supergraph technique and apply it to compute the one-loop divergenc...

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...

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...

We consider, in the harmonic superspace approach, the six-dimensional \( \mathcal{N} \) = (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...

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...

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...

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 tot...

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 betw...

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 d...

Using the Slavnov–Taylor identities we prove that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in all loops in supersymmetric gauge theories. This statement is verified by the explicit one-loop calculation made by the help of the BRST invariant version of the higher covariant derivative regu...

Using the Slavnov--Taylor identities we prove that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in all loops in ${\cal N}=1$ supersymmetric gauge theories. This statement is verified by the explicit one-loop calculation made by the help of the BRST invariant version of the higher covariant d...

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-...

Using the BRST invariant version of the higher covariant derivative regularization, we demonstrate that in N = 1 supersymmetric gauge theories the three-point vertices with two ghost legs and a single leg of the quantum gauge superfield are finite in all orders. This theorem is proved by the help of the Slavnov–Taylor identities and the supergraph...

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 a...

In the case of using the higher derivative regularization for N = 1 supersymmetric quantum electrodynamics (SQED) with N
f flavors, the loop integrals giving the β-function are integrals of double total derivatives in themomentum space. This feature allows reducing one of the loop integrals to an integral of the δ-function and deriving the Novikov–...

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...

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 high...

The Adler function D is found {\em exactly} in supersymmetric QCD. Our exact
formula relates D(Q^2) to the anomalous dimension of the matter superfields
\gamma (\alpha_s(Q^2)). En rout we prove another theorem: the absence of the
so-called singlet contribution to D. While such singlet contributions are
present in individual supergraphs, they cancel...

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...

The effective diagram technique based on the Schwinger-Dyson equations is constructed for \( \mathcal{N} \) = 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 β-function and the anomalous dimension of the matter superfields exactly in all loops,...

We briefly review the calculations of quantum corrections related with the
exact NSVZ $\beta$-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 i...

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 renormal...

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 hid...

The exact NSVZ $\beta$-function is obtained for ${\cal N}=1$ SQED with $N_f$
flavors in all orders of the perturbation theory, if the renormgroup functions
are defined in terms of the bare coupling constant and the theory is
regularized by higher derivatives. However, if the renormgroup functions are
defined in terms of the renormalized coupling co...

The exact NSVZ relation between a $\beta$-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 renorm...

## Citations

... The choice of the higher covariant derivative regularization is motivated by the fact that the NSVZ equation in supersymmetric theories is valid in all loops in the HD þ MSL scheme [44,45], so that the β-function in a certain loop can easily be obtained starting from the expressions for the anomalous dimensions of chiral matter superfields in the previous loops, see, e.g., [68,74,75]. Moreover, there are various versions of this regularization, which differ in the form of the higher derivative terms and the Pauli-Villars masses. ...

... The choice of the higher covariant derivative regularization is motivated by the fact that the NSVZ equation in supersymmetric theories is valid in all loops in the HD þ MSL scheme [44,45], so that the β-function in a certain loop can easily be obtained starting from the expressions for the anomalous dimensions of chiral matter superfields in the previous loops, see, e.g., [68,74,75]. Moreover, there are various versions of this regularization, which differ in the form of the higher derivative terms and the Pauli-Villars masses. ...

... By definition, in the HD þ MSL scheme a theory is regularized by higher covariant derivatives and divergences are removed by minimal subtraction of logarithms when only powers of ln Λ=μ (where Λ is the dimensionful regularization parameter and μ is a renormalization scale) are present in the renormalization constants, while all finite constants are set to 0. (The proof was based on the all-order perturbative derivation of the NSVZ β-function made in [47] for N ¼ 1 supersymmetric electrodynamics and in [45,48,49] for the N ¼ 1 non-Abelian supersymmetric theories. Its various parts have been verified and confirmed by numerous explicit calculations (see, e.g., [50][51][52][53][54][55][56][57][58]), some of them being made in such orders of the perturbation theory where the scheme dependence becomes essential.) ...

... By definition, in the HD þ MSL scheme a theory is regularized by higher covariant derivatives and divergences are removed by minimal subtraction of logarithms when only powers of ln Λ=μ (where Λ is the dimensionful regularization parameter and μ is a renormalization scale) are present in the renormalization constants, while all finite constants are set to 0. (The proof was based on the all-order perturbative derivation of the NSVZ β-function made in [47] for N ¼ 1 supersymmetric electrodynamics and in [45,48,49] for the N ¼ 1 non-Abelian supersymmetric theories. Its various parts have been verified and confirmed by numerous explicit calculations (see, e.g., [50][51][52][53][54][55][56][57][58]), some of them being made in such orders of the perturbation theory where the scheme dependence becomes essential.) ...

... This implies that the NSVZ equation is valid only for special renormalization prescriptions, which are usually called the NSVZ schemes. According to [35][36][37][38], these schemes constitute an infinite set and are related by finite renormalizations which satisfy a special constraint. A simple prescription giving some NSVZ schemes was obtained in the case of using the higher covariant derivative regularizaton [39][40][41] in the supersymmetric version [42,43]. ...

... In our previous work [40] we initiated the study of the two-loop divergent contribution to the effective action of 6D, N = (1, 1) SYM theory in the harmonic superfield formalism and calculated the divergent contributions proportional to 1 ε 2 in the gauge superfield sector of the model. In the present paper we will analyze the general structure of the two-loop divergent contributions to the effective action in both gauge and hypermultiplet sectors. ...

... By definition, in the HD þ MSL scheme a theory is regularized by higher covariant derivatives and divergences are removed by minimal subtraction of logarithms when only powers of ln Λ=μ (where Λ is the dimensionful regularization parameter and μ is a renormalization scale) are present in the renormalization constants, while all finite constants are set to 0. (The proof was based on the all-order perturbative derivation of the NSVZ β-function made in [47] for N ¼ 1 supersymmetric electrodynamics and in [45,48,49] for the N ¼ 1 non-Abelian supersymmetric theories. Its various parts have been verified and confirmed by numerous explicit calculations (see, e.g., [50][51][52][53][54][55][56][57][58]), some of them being made in such orders of the perturbation theory where the scheme dependence becomes essential.) ...

... This in particular implies that the DR scheme is NSVZ for N ¼ 2 supersymmetric gauge theories, at least, in the lowest orders. 2 However, it is known that the finiteness in the DR scheme does not in general ensure the finiteness for an arbitrary renormalization prescription. For instance, one-loop finite N ¼ 1 supersymmetric theories in the DR scheme are finite in the two-loop approximation [65], but are not two-loop finite for a general N ¼ 1 supersymmetric renormalization prescription [66]. Moreover, there are DR calculations for N ¼ 2 supersymmetric Yang-Mills theory in the component formulation which reveal the three-loop divergences. ...

... We use the abbreviations, s α (c α ) = sin α(cos α), s β (c β ) = sin β(cos β), t β = tan β, etc. We identify the physical state h as the SM-like observed Higgs boson of mass 125 GeV as all the Higgs signal strength measurements [45][46][47][48][49][50][51][52][53][54][55][56][57] are consistent with SM. Throughout the paper we collectively call H, A and H ± as the beyond SM (BSM) Higgs bosons. ...

... Higher loops are obtained as a result of certain "anomaly" in the measure revealing itself in the calculation of the second and higher loops, in analogy with Yang-Mills theory. 5 A general proof is presented in [8][9][10][11] while the direct perturbative all-loop calculations are given in [40][41][42]. One can complexify the coupling constants in the Lagrangians introducing their holomorphic counterpartners, ...