Abstract
Recent works have explored nonperturbative effects due to the existence of (infinitesimal) Gribov copies in Yang-Mills-Chern-Simons theories in three Euclidean dimensions. In particular, the removal of such copies modify the gauge field propagator by a self-consistent dynamically generated mass parameter, the Gribov parameter. Due to the interplay with the topological mass introduced by the Chern-Simons term, the propagator features a nontrivial set of phases with poles of different nature, leading to the possible interpretation of a confinfing to deconfining phase transition. Here, we restore the Becchi--Rouet--Stora--Tyutin (BRST) symmetry which is softly broken by the elimination of gauge copies and provide a BRST-invariant discussion of such a transition. In order to make clear all physical statements, we deal with linear covariant gauges which contain a gauge parameter and therefore allow for an explicit check of gauge parameter independence of physical results. We also discuss the generation of condensates due to the infrared relevance of infinitesimal Gribov copies.
Highlights
In this work we propose the quantization of YMCS theories in linear covariant gauges, i.e., gauges of the form (11)
We extended the elimination of infinitesimal Gribov copies in the linear covariant gauges
While in the Landau and maximal Abelian gauges the elimination breaks Becchi–Rouet–Stora– Tyutin (BRST) invariance, in this work we show how to restore it for color- and Lorentz-covariant linear gauges
Summary
The quantization of Yang-Mills theories in a continuum framework typically requires a gauge-fixing procedure. It can be expected that toward low energies (or growing coupling constant), the Faddeev-Popov procedure must be improved and replaced by another method which takes into account the existence of Gribov copies This has been achieved just for the infinitesimal copies, i.e., those generated by infinitesimal gauge transformations. In [30], it was realized that BRST invariance can be achieved by a suitable modification of the horizon function which corresponds to a dressing of the gauge field by a gauge-invariant variable Ahμ;a This has led to the proposal of a nonperturbative BRST quantization that takes into account the existence of (infinitesimal) Gribov copies in the gauge-fixing. We will apply such a quantization procedure to Yang-Mills-Chern-Simons (YMCS) theories quantized in the linear covariant gauges and inspect the consequences to the spectrum of the theory
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