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We pursue the study of SU(2) Euclidean Yang-Mills theory in the maximalAbelian gauge by taking into account the effects of the Gribov horizon. TheGribov approximation, previously introduced in [1], is improved through theintroduction of the horizon function, which is constructed under therequirements of localizability and renormalizability. By following Zwanziger'streatment of the horizon function in the Landau gauge, we prove that, when castin local form, the horizon term of the maximal Abelian gauge leads to aquantized theory which enjoys multiplicative renormalizability, a feature whichis established to all orders by means of the algebraic renormalization.Furthermore, it turns out that the horizon term is compatible with the localresidual U(1) Ward identity, typical of the maximal Abelian gauge, which iseasily derived. As a consequence, the nonrenormalization theorem,Z_{g}Z_{A}^{1/2}=1, relating the renormalization factors of the gauge couplingconstant Z_{g} and of the diagonal gluon field Z_{A}, still holds in thepresence of the Gribov horizon. Finally, we notice that a generalized dimensiontwo gluon operator can be also introduced. It is BRST invariant on-shell, aproperty which ensures its multiplicative renormalizability. Its anomalousdimension is not an independent parameter of the theory, being obtained fromthe renormalization factors of the gauge coupling constant and of the diagonalantighost field.Comment: 31 page

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Study of the maximal Abelian gauge in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>Euclidean Yang-Mills theory in the presence of the Gribov horizon

Study of the maximal Abelian gauge inSU(2)Euclidean Yang-Mills theory in the presence of the Gribov horizon