Abstract
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 parameterized by one finite function and one arbitrary constant. This implies that the NSVZ β-function remains unbroken if the finite renormalization of the coupling constant is related to the finite renormalization of the matter superfields by a special equation derived in this paper. The arbitrary constant corresponds to the arbitrariness of choosing the renormalization point. The results are illustrated by explicit calculations in the three-loop approximation.
Highlights
Supersymmetric quantum field theory models have many interesting properties
The NSVZ relation (1) for renormalization group functions (RGFs) defined in terms of the renormalized coupling constant is valid only in special subtraction schemes
If the regularization is made by the dimensional reduction method and the renormalization is made by the DR prescription, the NSVZ equation is obtained only after a specially tuned redefinition of the coupling constant
Summary
Supersymmetric quantum field theory models have many interesting properties. For example, supersymmetry leads to some non-renormalization theorems, which sometimes produce very non-trivial relations between various renormalization constants. Eq (1) is written for the former RGFs, because below in this paper we will mostly deal with them It is known [10, 11] that for Abelian supersymmetric theories RGFs defined in terms of the bare coupling constant α0 satisfy the NSVZ relation in all orders in the case of using the higher derivative (HD) regularization [12, 13] in the supersymmetric version [14, 15]. Most calculations with dimensional reduction were made in the DR scheme which is analogous to the MS scheme for the dimensional regularization In this case the NSVZ equation is not valid already in the lowest order where the scheme dependence is essential (namely, for the three-loop β-function and the two-loop anomalous dimension) [29]. One of them is obtained starting from the DR result by a finite renormalization (only) of the coupling constant, and the other is obtained with the help of the higher derivative regularization supplemented by the boundary conditions (2)
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