On the zero modes of the Faddev-Popov operator in the Landau gauge

Abstract: Following Henyey procedure, we construct examples of zero modes of the Faddev-Popov operator in the Landau gauge in Euclidean space in D dimensions, for both SU(2) and SU(3 groups. We consider gauge field configurations $A<sup>a_\mu$ which give rise to a field strength, $$F^a_{\mu\nu} =\partial_\mu A^a_\nu -\partial_\nu A^a_\mu + f^{{abc}A^b_\mu} A<sup>c_\nu$$, whose nonlinear term, $f^{{abc}A^b_\mu} A<sup>c_\nu$, turns out to be nonvanishing. To our knowledge, this is the first time where such a non-abelian configuration is explicitly obtained in the case of SU(3) in 4D.