Higher derivative regularization and quantum corrections in N=1 supersymmetric theories

TL;DR

This paper reviews the use of higher covariant derivative regularization in N=1 supersymmetric theories, showing that quantum correction integrals are total derivatives and discussing derivation of the exact beta function.

Contribution

It demonstrates that all integrals for the Gell-Mann--Low function are total derivatives and introduces an identity for Green functions in N=1 supersymmetric theories.

Findings

All integrals defining the Gell-Mann--Low function are total derivatives.

An identity for Green functions in N=1 supersymmetric theories is established.

Methods for deriving the exact beta function are discussed.

Abstract

We review some results of applying the higher covariant derivative regularization to the investigation of quantum corrections structure in N=1 supersymmetric theories. In particular, we demonstrate that all integrals, defining the Gell-Mann--Low function in supersymmetric theories, are integrals of total derivatives. As a consequence, there is an identity for Green functions, which does not follow from any known symmetry of the theory, in N=1 supersymmetric theories. We also discuss how to derive the exact $\beta$-function by methods of the perturbation theory.