Study of the properties of the Gribov region in SU(N) Euclidean Yang-Mills theories in the maximal Abelian gauge

Abstract

In this paper we address the issue of the Gribov copies in SU(N), N>2, Euclidean Yang-Mills theories quantized in the maximal Abelian gauge. A few properties of the Gribov region in this gauge are established. Similarly to the case of SU(2), the Gribov region turns out to be convex, bounded along the off-diagonals directions in field space, and unbounded along the diagonal ones. The implementation of the restriction to the Gribov region in the functional integral is discussed through the introduction of the horizon function, whose construction will be outlined in detail. The influence of this restriction on the behavior of the gluon and ghost propagators of the theory is also investigated together with a set of dimension two condensates.

43 pages, published version

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Cited by in corpus (7)

• Dimension two condensates in the Gribov-Zwanziger theory in the Coulomb gauge
• Yang-Mills theory in the maximal Abelian gauge in presence of scalar matter fields
• Study of Gribov Copies in the Yang-Mills ensemble
• Hints of (de)confinement in Yang-Mills-Chern-Simons theories in the maximal Abelian gauge
• Quantization of Yang-Mills Theories without the Gribov Ambiguity
• The gap equations of background field invariant Refined Gribov-Zwanziger action proposals and the deconfinement transition
• Gauge copies and the fate of background independence in Yang-Mills theories: a leading order analysis