Three-loop renormalization of the N=1, N=2, N=4 supersymmetric Yang-Mills theories

TL;DR

This paper performs a three-loop calculation of renormalization constants in N=1, N=2, N=4 supersymmetric Yang-Mills theories, confirming the consistency of the dimensional reduction scheme at this order.

Contribution

It provides the first three-loop renormalization constants for these theories, demonstrating the scheme's validity up to third order in perturbation theory.

Findings

Beta-functions for N=1 and N=4 SYM are identical from different vertices.

Dimensional reduction scheme remains consistent up to three loops.

Results support the scheme's applicability in supersymmetric gauge theories.

Abstract

We calculate the renormalization constants of the N=1, N=2, N=4 supersymmetric Yang-Mills theories in an arbitrary covariant gauge in the dimensional reduction scheme up to three loops. We have found, that the beta-functions for N=1 and N=4 SYM theories are the same from the different triple vertices. This means that the dimensional reduction scheme works correctly in these models up to third order of perturbative theory.