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.

arXiv comment31 pages

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• Non-perturbative treatment of the linear covariant gauges by taking into account the Gribov copies
• Gribov horizon and non-perturbative BRST symmetry in the maximal Abelian gauge
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• A study of the lightest glueball states in SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge
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• Gribov as a Phase Transition
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• Two-dimensional gluon propagators in maximally Abelian gauge in SU(2) Lattice QCD
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• 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
• Non-perturbative aspects of Yang-Mills theories
• Study of the all orders multiplicative renormalizability of a local matter confining Gribov-Zwanziger action in the MAG
• Infrared behavior of the gluon and ghost propagators in Yang-Mills theories