Ultraviolet divergences in supersymmetric theories regularized by higher derivatives

TL;DR

This paper explores how higher covariant derivative regularization in ${\ m N}=1$ supersymmetric gauge theories reveals exact relations like the NSVZ equation, connecting the beta function and anomalous dimensions across all loops.

Contribution

It demonstrates that higher covariant derivative regularization naturally leads to the derivation of the NSVZ relation in supersymmetric gauge theories.

Findings

Higher covariant derivative regularization reveals exact RG relations.

The NSVZ equation is derived and shown to hold at all loops.

A simple renormalization scheme consistent with the NSVZ relation is constructed.

Abstract

Structure of quantum corrections in ${\cal N}=1$ supersymmetric gauge theories is investigated in the case of using the regularization by higher covariant derivatives. It is demonstrated that this regularization allows revealing some interesting features which lead to the exact relations between the renormalization group functions. In particular, the NSVZ equation, which relates the $\beta$-function to the anomalous dimension of the matter superfields, naturally appears in this case. We briefly review the all-loop derivation of this equation and the construction of a simple renormalization prescription under which it is valid.