Multiloop calculations in supersymmetric theories with the higher covariant derivative regularization

TL;DR

This paper explores the use of higher covariant derivative regularization in supersymmetric theories, highlighting its consistency over dimensional reduction and its role in deriving the NSVZ beta-function through total derivative integrals.

Contribution

It demonstrates that higher covariant derivative regularization can be effectively applied to supersymmetric theories and explains the origin of the NSVZ beta-function via total derivative integrals.

Findings

Integrals for the beta-function can be expressed as total derivatives.

The regularization preserves supersymmetry more reliably than dimensional reduction.

Numerical methods are needed to compute anomalous dimensions.

Abstract

Most calculations of quantum corrections in supersymmetric theories are made with the dimensional reduction, which is a modification of the dimensional regularization. However, it is well known that the dimensional reduction is not self-consistent. A consistent regularization, which does not break the supersymmetry, is the higher covariant derivative regularization. However, the integrals obtained with this regularization can not be usually calculated analytically. We discuss application of this regularization to the calculations in supersymmetric theories. In particular, it is demonstrated that integrals defining the beta-function are possibly integrals of total derivatives. This feature allows to explain the origin of the exact NSVZ beta-function, relating the beta-function with the anomalous dimensions of the matter superfields. However, integrals for the anomalous dimension should be calculated numerically.