Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

V. N. Velizhanin

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.

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

Paper Structure

This paper contains 3 sections, 14 equations.

Table of Contents

  1. Note added Februar, 2026 When this mismatch was corrected, we received information that the zero three-loop coefficient in the Yukawa beta function for ${\mathcal{N}}=2$ SYM theory was obtained in Ref
  2. Acknowledgements
  3. Appendix: Renormalization constants