The higher covariant derivative regularization as a tool for revealing the structure of quantum corrections in supersymmetric gauge theories

TL;DR

This paper reviews how the higher covariant derivative regularization technique helps analyze quantum corrections in supersymmetric gauge theories, revealing the structure of the beta function and simplifying calculations.

Contribution

It demonstrates the effectiveness of the higher covariant derivative regularization in deriving the NSVZ beta function and non-renormalization theorems in supersymmetric gauge theories.

Findings

Beta function expressed as integrals of double total derivatives

Construction of the NSVZ renormalization prescription in all loops

Explicit two-loop calculation illustrating the method

Abstract

We discuss why the Slavnov higher covariant derivative regularization appeared to be an excellent instrument for investigating quantum corrections in supersymmetric gauge theories. For example, it allowed to demonstrate that the $\beta$-function in these theories is given by integrals of double total derivatives and to construct the NSVZ renormalization prescription in all loops. It was also used for deriving the non-renormalization theorem for the triple gauge-ghost vertices. With the help of this theorem the exact NSVZ $\beta$-function was rewritten in a new form, which revealed its perturbative origin. Moreover, in the case of using the higher covariant derivative regularization it is possible to construct a method for obtaining the $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories, which simplifies the calculations in a great extent. This method is illustrated by an explicit two-loop calculation made in the general $\xi$-gauge.