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

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 $A_{\mu }^a$ which give rise to a field strength, $F^a_{\mu\nu} =\partial_\mu A^a_\nu -\partial_\nu A^a_\mu + f^{abc}A^b_\mu A^c_\nu$,whosenonlinearterm,$ f^{abc}A^b_\mu A^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.