  Recently, it has been observed that the non-Abelian action associated with
lattice monopoles and vortices is ultraviolet divergent, at least at presently
available lattices. On the other hand, the total length of the monopole
trajectories and area of the vortices scale in physical units. Coexistence of
the two different scales, infrared and ultraviolet, for the same vacuum
fluctuations represents a fine tuning. To check consistency of the newly
emerging picture of non--perturbative fluctuations we consider constraints from
the continuum theory on the ultraviolet behaviour of the monopoles and
vortices. The constraints turn to be satisfied by the data in a highly
non-trivial way. Namely, it is crucial that the monopoles populate not the
whole of the four dimensional space but a two-dimensional subspace of it.
