Instantons and Gribov copies in the maximally Abelian gauge

We calculate the Faddeev-Popov operator corresponding to the maximally Abel ian gauge for gauge group SU(N). Specializing to SU(2) we look for explicit zero modes of this operator. Within an illuminating toy model (Yang-Mills mechanics) the problem can be completely solved and understood. In the held theory case we are able to find an analytic expression for a normalizable zero mode in the background of a single 't Hooft instanton. Accordingly, su ch an instanton corresponds to a horizon configuration in the maximally Abe lian gauge. Possible physical implications are discussed. (C) 2000 Elsevier Science B.V. All rights reserved.