A gauge invariant infrared stabilization of 3D Yang-Mills gauge theories

TL;DR

This paper introduces an infrared stabilization method for 3D Yang-Mills theories using a gauge-invariant operator and the inversion method, providing unambiguous numerical results without renormalization ambiguities.

Contribution

The work demonstrates the gauge invariance and renormalizability of a nonlocal operator in 3D gauge theories, enabling infrared stabilization and identification of new renormalizable operators.

Findings

Infrared stabilization achieved using the inversion method with the $A^2$ operator.

The theory is ultraviolet finite in dimensional regularization, removing renormalization scheme dependence.

Identification of a set of power-counting renormalizable nonlocal operators of dimension two.

Abstract

We demonstrate that the inversion method can be a very useful tool in providing an infrared stabilization of 3D gauge theories, in combination with the mass operator $A^2$ in the Landau gauge. The numerical results will be unambiguous, since the corresponding theory is ultraviolet finite in dimensional regularization, making a renormalization scale or scheme obsolete. The proposed framework is argued to be gauge invariant, by showing that the nonlocal gauge invariant operator $A^2_{\min}$, which reduces to $A^2$ in the Landau gauge, could be treated in 3D, in the sense that it is power counting renormalizable in any gauge. As a corollary of our analysis, we are able to identify a whole set of powercounting renormalizable nonlocal operators of dimension two.