Local and renormalizable framework for the gauge-invariant operatorAmin2in Euclidean Yang-Mills theories in linear covariant gauges

Abstract

We address the issue of the renormalizability of the gauge-invariant non-local dimensiontwo operator A 2 min , whose minimization is defined along the gauge orbit. Despite its non-local character, we show that the operator A 2 min can be cast in local form through the introduction of an auxiliary Stueckelberg field. The localization procedure gives rise to an unconventional kind of Stueckelberg-type action which turns out to be renormalizable to all orders of perturbation theory. In particular, as a consequence of its gauge invariance, the anomalous dimension of the operator A 2 min turns out to be independent from the gauge parameter α entering the gauge-fixing condition, being thus given by the anomalous dimension of the operator A 2 in the Landau

A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

“…This was achieved by the introduction of the suitable gauge-invariant fields A h , φ h and ψ h , see [1][2][3][4][5], which, albeit local, are non-polynomial in the auxiliary Stueckelberg-type field ξ a . Nevertheless, such variables as well as the proposed non-perturbative matter coupling give rise to a local ation which can be proven to be renormalizable to all orders, see [70,81].…”

Study of a gauge invariant local composite fermionic field

“…As pointed out in details in [31,45], the action (10) displays deep differences with respect to the conventional non-renormalizable non-Abelian Stueckelberg action [41][42][43][44]. The difference lies precisely in the transversality constraint (5), implemented in expression (10) through the fields (τ,η, η).…”

“…Condition (5) follows directly from the minimization procedure for the operator A 2 min . As such, it has a geometrical meaning while being responsible for a good ultraviolet behavior of the model which, unlike the case of the standard Stueckelberg action, enjoys in fact perturbative renormalizability [31,45].…”

“…The quantities F a µ (A, ξ), G a µ (A, ξ), I(A, ξ) and I (A, ξ) have been already worked out in [31,32], being given by…”

“…The minimization procedure for A 2 min enables one to introduce a nonlocal gauge field A h µ which turns out to be left invariant by gauge transformations, order by order in powers of the coupling g [38]. Recently, a localization procedure for A h µ has been achieved by means of a localizing Stueckelberg-like field ξ [31,32]. The resulting non-polynomial action has been proven to be renormalizable to all orders thanks to the existence of a Becchi-Rouet-Stora-Tyutin (BRST) nilpotent exact symmetry.…”