Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge

• We study the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge.
• For d=2d=2 we obtain solutions with finite action but not finite Hilbert norm.
• For d=3,4d=3,4 we obtain solutions with finite action and finite Hilbert norm.
• These results can be compared with those previously obtained in the Landau gauge.

A study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge is presented in the case of the gauge group SU(2)SU(2) and for different Euclidean space–time dimensions. Explicit examples of classes of normalizable zero modes and corresponding gauge field configurations are constructed by taking into account two boundary conditions, namely: (i) the finite Euclidean Yang–Mills action, (ii) the finite Hilbert norm.