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

Abstract

The dimension two gauge invariant non-local operator $A_{\min }^2$, obtained through the minimization of $\int d^{4}x{A}^2$ along the gauge orbit, allows to introduce a non-local gauge invariant configuration $A_{\mu }^h$ 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 $A_{\mu }^h$ 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.

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• Dynamically massive linear covariant gauges: setup and first results
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• Landau-Khalatnikov-Fradkin transformations for the two loop massless quark propagator
• Study of a gauge invariant local composite fermionic field
• On the renormalization of a generalized supersymmetric version of the maximal Abelian gauge
• One-loop analytic structure of the deep-infrared Landau-gauge gluon propagator at finite temperature