On a renormalizable class of gauge fixings for the gauge invariant operator $A_{\min }^{2}$

TL;DR

This paper introduces a renormalizable class of gauge fixings for the gauge invariant operator $A_{ ext{min}}^2$, enabling a local, BRST invariant formulation useful for studying non-perturbative infrared effects in confining gauge theories.

Contribution

It develops a fully local, BRST invariant formulation of the gauge invariant operator $A_{ ext{min}}^2$, ensuring all-order renormalizability and providing a new approach to infrared analysis in gauge theories.

Findings

The formulation is fully local and BRST invariant.

The resulting action is renormalizable at all orders.

A class of covariant gauge fixings introduces a mass for the Stueckelberg field.

Abstract

The dimension two gauge invariant non-local operator $A_{\min }^{2}$, obtained through the minimization of $\int d^4x A^2$ along the gauge orbit, allows to introduce a non-local gauge invariant configuration $A^h_\mu$ which can be employed to built up a class of Euclidean massive Yang-Mills models useful to investigate non-perturbative infrared effects of confining theories. A fully local setup for both $A_{\min }^{2}$ and $A^{h}_\mu$ can be achieved, resulting in a local and BRST invariant action which shares similarities with the Stueckelberg formalism. Though, unlike the case of the Stueckelberg action, the use of $A_{\min }^{2}$ gives rise to an all orders renormalizable action, a feature which will be illustrated by means of a class of covariant gauge fixings which, as much as 't Hooft's $R_\zeta$-gauge of spontaneously broken gauge theories, provide a mass for the Stueckelberg field.