Dimensional Reduction Applied to Non-Supersymmetric Theories

TL;DR

This paper investigates the use of Dimensional Reduction for regularising non-supersymmetric Yang-Mills theories, computing anomalous dimensions to four-loop order, and emphasizing the treatment of evanescent couplings to ensure accurate results.

Contribution

It provides a detailed four-loop analysis of anomalous dimensions in non-supersymmetric theories using DRED, highlighting the importance of evanescent couplings and confirming supersymmetry preservation in Super-Yang-Mills.

Findings

Evanescent couplings must be carefully distinguished from real couplings.

Dimensional Reduction preserves supersymmetry in Super-Yang-Mills calculations.

Anomalous dimensions are computed up to four-loop order.

Abstract

We consider regularisation of a Yang-Mills theory by Dimensional Reduction (DRED). In particular, the anomalous dimensions of fermion masses and gauge coupling are computed to four-loop order. We put special emphasis on the treatment of evanescent couplings which appear when DRED is applied to non-supersymmetric theories. We highlight the importance of distinguishing between the evanescent and the real couplings. Considering the special case of a Super-Yang-Mills theory, we find that Dimensional Reduction is sufficient to preserve Supersymmetry in our calculations.