Properties of Gribov region and horizon function in the SU(N) Maximal Abelian Gauge

Full text: The problem of the Gribov copies deals with the impossibility of to choose a unique gauge condition in the quantization process in the Yang Mills theories. In the Landau gauge, several properties of the Gribov region are established, the implementation of the Gribov copies in the path integral is taking account by the introduction of the horizon function directly in the action giving rise to modifications in the ghost and gluon propagator in the infrared regime. However, is interesting to looking at other gauge choices for obtain additional information of the phenomena, and compare our results in the landau gauge. In this work 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. (author)