A study of the maximal Abelian gauge in SU(2) Euclidean Yang-Mills theory in the presence of the Gribov horizon

Abstract

We pursue the study of SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge by taking into account the effects of the Gribov horizon. The Gribov approximation, previously introduced in [1], is improved through the introduction of the horizon function, which is constructed under the requirements of localizability and renormalizability. By following Zwanziger's treatment of the horizon function in the Landau gauge, we prove that, when cast in local form, the horizon term of the maximal Abelian gauge leads to a quantized theory which enjoys multiplicative renormalizability, a feature which is established to all orders by means of the algebraic renormalization. Furthermore, it turns out that the horizon term is compatible with the local residual U(1) Ward identity, typical of the maximal Abelian gauge, which is easily derived. As a consequence, the nonrenormalization theorem, Z_{g}Z_{A}^{1/2}=1, relating the renormalization factors of the gauge coupling constant Z_{g} and of the diagonal gluon field Z_{A}, still holds in the presence of the Gribov horizon. Finally, we notice that a generalized dimension two gluon operator can be also introduced. It is BRST invariant on-shell, a property which ensures its multiplicative renormalizability. Its anomalous dimension is not an independent parameter of the theory, being obtained from the renormalization factors of the gauge coupling constant and of the diagonal antighost field.

31 pages

References in corpus (2)

• Effects of the quark field on the ghost propagator of Lattice Landau Gauge QCD
• Quantum properties of a non-Abelian gauge invariant action with a mass parameter

Cited by in corpus (16)

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• Dimension two condensates in the Gribov-Zwanziger theory in the Coulomb gauge
• Nonperturbative ghost dynamics in the maximal Abelian 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
• Gauge copies and the fate of background independence in Yang-Mills theories: a leading order analysis
• Two-dimensional gluon propagators in maximally Abelian gauge in SU(2) Lattice QCD
• Study of the nonlocal gauge invariant mass operator $\mathrm{Tr}\int d^{4}x{F}_{\mu \nu }(D^2{)}^{-1}{F}_{\mu \nu }$ in the maximal Abelian gauge
• Local renormalizable gauge theories from nonlocal operators
• Non-perturbative aspects of Yang-Mills theories
• Infrared behavior of the gluon and ghost propagators in Yang-Mills theories