NSVZ relation and the dimensional reduction in $\mathcal{N}=1$ SQED

Abstract

It is known that factorization of the $\beta$-function loop integrals into integrals of double total derivatives is an important ingredient needed for deriving the NSVZ relation by direct perturbative calculations in $\mathcal{N}=1$ SQED regularized by the higher derivatives. It allows to relate the $\beta$-function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant. In this work we find the analog of this result in the case of using dimensional reduction regularization in the lowest orders. However, we demonstrate that in this case the NSVZ relation is not satisfied for the RG functions defined in terms of the bare coupling constant. Nevertheless, it is possible to impose boundary conditions to the renormalization constants determining the NSVZ scheme in the three-loop order for the RG functions defined in terms of the renormalized coupling constant.

4 pages, contribution to the Proceedings of the International Workshop "Supersymmetries and Quantum Symmetries" (SQS'2017, 31 July - 5 August, 2017)

References in corpus (4)

• Derivation of the exact NSVZ beta-function in N=1 SQED, regularized by higher derivatives, by direct summation of Feynman diagrams
• The NSVZ beta-function and the Schwinger-Dyson equations for N=1 SQED with N_f flavors, regularized by higher derivatives
• The NSVZ scheme for $\mathcal{N}=1$ SQED with $N_f$ flavors, regularized by the dimensional reduction, in the three-loop approximation
• Structure of three-loop contributions to the beta-function of N=1 SQED with N_f flavors, regularized by the dimensional reduction