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We point out the existence of a nonperturbative exact nilpotent BRST symmetry for the Gribov-Zwanziger action in the Landau gauge. We then put forward a manifestly BRST invariant resolution of the Gribov gauge fixing ambiguity in the linear covariant gauge. [ABSTRACT FROM AUTHOR]

We address the issue of the all order multiplicative renormalizability of SU(2) Yang-Mills theories quantized in the maximal Abelian gauge in presence of scalar matter fields. The nonlinear character of the maximal Abelian gauge requires the introduction of quartic interaction terms in the Faddeev-Popov ghosts, a well-known feature of this gauge. We show that, when scalar matter fields are introduced, a second quartic interaction term between scalar fields and Faddeev-Popov ghosts naturally arises. A Becchi-Rouet-Stora- Tyutin invariant action accounting for those quartic interaction terms is identified and proven to be multiplicative renormalizable to all orders by means of the algebraic renormalization procedure. [ABSTRACT FROM AUTHOR]

Recently, based on a new procedure to quantize the theory in the continuum, it was argued that Singer's theorem points toward the existence of a Yang-Mills ensemble. In the new approach, the gauge fields are mapped into an auxiliary field space used to initially determine sectors labeled by center vortices, and then separately fix the gauge on them. In this work, we study this procedure in more detail. We provide examples of configurations belonging to these sectors and discuss the existence of non-Abelian degrees of freedom. Then, we discuss the importance of the mapping injectivity, and show that this property holds infinitesimally for typical configurations of the vortex-free sector and for the simplest example in the one-vortex sector. Finally, we show that these examples are free from Gribov copies. [ABSTRACT FROM AUTHOR]

In this work, we analyze a recent proposal to detect SU(N) continuum Yang-Mills sectors labeled by center vortices, inspired by Laplacian-type center gauges in the lattice. Initially, after the introduction of appropriate external sources, we obtain a rich set of sector-dependent Ward identities, which can be used to control the form of the divergences. Next, we show the all-order multiplicative renormalizability of the center-vortex free sector. These are important steps towards the establishment of a first-principles, well-defined, and calculable Yang-Mills ensemble. [ABSTRACT FROM AUTHOR]

The refined Gribov-Zwanziger framework takes into account the existence of equivalent gauge field configurations in the gauge-fixing quantization procedure of Euclidean Yang-Mills theories. Recently, this setup was extended to the family of linear covariant gauges giving rise to a local and Becchi-Rouet-Stora-Tyutin (BRST)-invariant action. In this paper, we give an algebraic proof of the renormalizability of the resulting action to all orders in perturbation theory. [ABSTRACT FROM AUTHOR]

We address the issue of the renormalizability of the gauge-invariant nonlocal dimension-two operator Amin², whose minimization is defined along the gauge orbit. Despite its nonlocal character, we show that the operator Amin² 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 that 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 Amin² turns out to be independent from the gauge parameter α entering the gauge-fixing condition, thus being given by the anomalous dimension of the operator A² in the Landau gauge. [ABSTRACT FROM AUTHOR]

In order to construct a gauge-invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge-invariant transverse configurations A h. Such configurations can be obtained through the minimization of the functional A 2 min along the gauge orbit within the BRST-invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of nonperturbative aspects of the theory in a BRST-invariant and gauge-parameter-independent way. In particular, it turns out that the poles of ⟨ A h μ (k) A h ν (-k) ⟩ are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter α entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST-invariant formulation introduced before. Moreover, the correlator ⟨ A h μ (k) A h ν (-k) ⟩ enables us to attach a BRST-invariant meaning to the possible positivity violation of the corresponding temporal Schwinger correlator, giving thus for the first time a consistent, gauge parameter independent, setup to adopt the positivity violation of ⟨ A h μ (k) A h ν (-k) ⟩ as a signature for gluon confinement. Finally, in the context of gauge theories supplemented with a fundamental Higgs field, we use ⟨ A h μ (k) A h ν (-k) ⟩ to probe the pole structure of the massive gauge boson in a gauge-invariant fashion. [ABSTRACT FROM AUTHOR]