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

TL;DR

This paper develops an effective diagram technique for N=1 SQED with N_f flavors, using higher derivative regularization, to derive the exact NSVZ relation between the beta-function and anomalous dimensions in all loops.

Contribution

It introduces a new diagrammatic approach based on Schwinger-Dyson equations for deriving the NSVZ relation in N=1 SQED with higher derivative regularization.

Findings

All beta-function integrals are double total derivatives.

Verified identities relating Green functions.

Exact NSVZ relation holds in all loops.

Abstract

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.