Local renormalizable gauge theories from nonlocal operators

TL;DR

This paper explores nonlocal operators in Yang-Mills theories, showing they can be made local and renormalizable through auxiliary fields, potentially impacting the understanding of confinement.

Contribution

It demonstrates that certain nonlocal operators can be localized and used to construct renormalizable gauge theories, expanding the toolkit for quantum field theory.

Findings

Identification of a class of nonlocal operators leading to renormalizable theories

Localization achieved via auxiliary fields preserving symmetry

Detailed analysis of the operator $rac{1}{D^2}$ in Yang-Mills

Abstract

The possibility that nonlocal operators might be added to the Yang-Mills action is investigated. We point out that there exists a class of nonlocal operators which lead to renormalizable gauge theories. These operators turn out to be localizable by means of the introduction of auxiliary fields. The renormalizability is thus ensured by the symmetry content exhibited by the resulting local theory. The example of the nonlocal operator $\int A \frac{1}{D^2} A $ is analysed in detail. A few remarks on the possible role that these operators might have for confining theories are outlined.