Gribov horizon and non-perturbative BRST symmetry in the maximal Abelian gauge

The non-perturbative nilpotent exact BRST symmetry of the Gribov-Zwanziger action in the Landau gauge constructed in [ arXiv:1506.06995 [hep-th]] is generalized to the case of Euclidean Yang-Mills theories quantized in the maximal Abelian gauge. The resulting diagonal gluon propagator is evaluating in dimensions D=4,3,2. In D=4,3 a decoupling type behavior is found in the infrared region, while in D=2 a scaling type behavior emerges.Comment: Reviewed version with a new section and new references adde

Interpolating among the Landau, Coulomb and maximal Abelian gauges

A generalized gauge fixing which interpolates among the Landau, Coulomb and maximal Abelian gauges is constructed.Comment: Final version, to appear in Rapid Communication in Physical Review D. Added remarks and reference

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

In this work, we study the propagators of matter fields within the framework of the Refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the Refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST invariant formulation of the Gribov-Zwanziger framework achieved in [Capri et al 2016], the propagators of scalar and quark fields in the adjoint and fundamental representations of the gauge group are worked out explicitly in the linear covariant, Curci-Ferrari and maximal Abelian gauges. Whenever lattice data are available, our results exhibit good qualitative agreement.Comment: 27 pages, no figures; V2, minor modifications, to appear in EPJ

An all-order proof of the equivalence between Gribov's no-pole and Zwanziger's horizon conditions

The quantization of non-Abelian gauge theories is known to be plagued by Gribov copies. Typical examples are the copies related to zero modes of the Faddeev-Popov operator, which give rise to singularities in the ghost propagator. In this work we present an exact and compact expression for the ghost propagator as a function of external gauge fields, in SU(N) Yang-Mills theory in the Landau gauge. It is shown, to all orders, that the condition for the ghost propagator not to have a pole, the so-called Gribov's no-pole condition, can be implemented by demanding a nonvanishing expectation value for a functional of the gauge fields that turns out to be Zwanziger's horizon function. The action allowing to implement this condition is the Gribov-Zwanziger action. This establishes in a precise way the equivalence between Gribov's no-pole condition and Zwanziger's horizon condition.Comment: 11 pages, typos corrected, version accepted for publication in Phys. Lett.