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

Understand

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.