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

2020

J. High Energ. Phys.

Self Cite

The two-loop anomalous dimension of the chiral matter superfields is calculated for a general 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 prescription. For the one-loop finite theories we find a simple relation between the higher derivative regulators under which the anomalous dimension defined in terms of the bare couplings vanishes in the considered approximation. In this case the one-loop finite theory is also two-loop finite in the HD+MSL scheme. Using the assumption that with the higher covariant derivative regularization the NSVZ equation is satisfied for RGFs defined in terms of the bare couplings, we construct the expression for the three-loop β-function. Again, the result is written both for the β-function defined in terms of the bare couplings and for the one defined in terms of the renormalized couplings for an arbitrary renormalization prescription.

Section: Introductionmentioning

confidence: 99%

Two-loop renormalization of the matter superfields and finiteness of $$ \mathcal{N} $$ = 1 supersymmetric gauge theories regularized by higher derivatives

Kazantsev

2020

J. High Energ. Phys.

Self Cite

“…Also the higher covariant derivative regularization is a very important ingredient needed for the all-loop perturbative derivation of the NSVZ β-function. According to [63][64][65][66], summing the perturbation series we do not obtain the original form of the NSVZ equation. Instead of it we obtain the relation between the L-loop β-function and the (L − 1)-loop anomalous dimensions of the quantum gauge superfield, of the Faddeev-Popov ghosts, and of the matter superfields.…”

Section: Discussionmentioning

confidence: 99%

“…(The sums of ghost and matter singularities have also been calculated by a different method in ref. [66].) As the result, the NSVZ equation (1.4) is obtained for the renormalization group functions (RGFs) defined in terms of the bare couplings for an arbitrary renormalization prescription supplementing the higher covariant derivative regularization.…”

Section: Jhep10(2021)046mentioning

confidence: 99%

The NSVZ relations for $$ \mathcal{N} $$ = 1 supersymmetric theories with multiple gauge couplings

Korneev

Плотников

et al. 2021

J. High Energ. Phys.

Self Cite

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 demonstrate that the NSVZ-like equation for the Adler D-function follows from the NSVZ relations. Also we derive all-loop equations describing how the NSVZ equations for theories with multiple gauge couplings change under finite renormalizations. They allow describing a continuous set of NSVZ schemes in which the exact NSVZ β-functions are valid for all gauge coupling constants. Very likely, this class includes the HD+MSL scheme, which is obtained if a theory is regularized by Higher covariant Derivatives and divergences are removed by Minimal Subtractions of Logarithms. That is why we also discuss how one can construct the higher derivative regularization for theories with multiple gauge couplings. Presumably, this regularization allows to derive the NSVZ equations for such theories in all loops. In this paper we make the first step of this derivation, namely, the NSVZ equations for theories with multiple gauge couplings are rewritten in a new form which relates the β-functions to the anomalous dimensions of the quantum gauge superfields, of the Faddeev-Popov ghosts, and of the matter superfields. The equivalence of this new form to the original NSVZ relations follows from the extension of the non-renormalization theorem for the triple gauge-ghost vertices, which is also derived in this paper.

“…Then they are reduced to the sums of singularities which correspond to various cuts of internal lines in vacuum supergraphs. These sums were calculated in all orders in [29] (see also [71]). The result can be presented in the following form:…”

Section: Summation Of Singular Contributionsmentioning

confidence: 99%

NSVZ Relation in Supersymmetric Theories Regularized by Higher Derivatives

2018

Phys. Part. Nuclei

Self Cite

Structure of quantum corrections in 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, the NSVZ equation, which relates the β-function to the anomalous dimension of the matter superfields, naturally appears in this case. We briefly review the all-loop derivation of this equation and the construction of a simple renormalization prescription under which it is valid.