The NSVZ beta-function in supersymmetric theories with different regularizations and renormalization prescriptions

TL;DR

This paper reviews the derivation of the NSVZ beta-function in ${ m N}=1$ supersymmetric theories, focusing on scheme dependence, regularization methods, and how to achieve exact relations in different renormalization schemes.

Contribution

It explains how to obtain the NSVZ relation using higher derivative regularization and constructs a scheme that ensures the relation holds exactly in all orders for Abelian theories.

Findings

NSVZ beta-function derived using higher derivative regularization

A special renormalization scheme ensures exact NSVZ relation in Abelian theories

Scheme independence of the NSVZ beta-function in non-Abelian theories

Abstract

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 if a theory is regularized by higher derivatives. Also we describe, how to construct a special renormalization prescription which gives the NSVZ relation for the renormalization group functions defined in terms of the renormalized coupling constant exactly in all orders for Abelian supersymmetric theories, regularized by higher derivatives. The scheme dependence of the NSVZ $\beta$-function (for the renormalization group functions defined in terms of the renormalized coupling constant) is discussed in the non-Abelian case. It is shown that in this case the NSVZ $\beta$-function leads to a certain scheme-independent equality.