On the gauge-invariant operator $A^2_{\min}$ in Euclidean Yang-Mills theories

TL;DR

This paper reviews the gauge-invariant operator $A^2_{min}$ in Euclidean Yang-Mills theories, showing how it can be localized via an auxiliary field and remains renormalizable at all orders.

Contribution

It introduces a local formulation of the non-local operator $A^2_{min}$ using a Stueckelberg field, ensuring all-order renormalizability.

Findings

The operator $A^2_{min}$ can be expressed locally with an auxiliary field.

The resulting local action is proven to be renormalizable to all orders.

The approach provides a gauge-invariant, non-local operator with a local, renormalizable formulation.

Abstract

We review our recent work on the gauge-invariant non-local dimension-two operator $A^2_{\rm min}$, whose minimization is defined along the gauge orbit. Albeit non-local, the operator $A^2_{\rm min}$ can be cast in local form through the introduction of an auxiliary Stueckelberg field. The whole procedure results into a local action which turns out to be renormalizable to all orders.