  Two popular perspectives on the non-perturbative domain of Yang-Mills
theories are either in terms of the gluons themselves or in terms of collective
gluonic excitations, i.e. topological excitations. If both views are correct,
then they are only two different representations of the same underlying
physics. One possibility to investigate this connection is by the determination
of gluon correlation functions in topological background fields, as created by
the smearing of lattice configurations. This is performed here for the minimal
Landau gauge gluon propagator, ghost propagator, and running coupling, both in
momentum and position space for SU(2) Yang-Mills theory. The results show that
the salient low-momentum features of the propagators are qualitatively retained
under smearing at sufficiently small momenta, in agreement with an equivalence
of both perspectives. However, the mid-momentum behavior is significantly
affected. These results are also relevant for the construction of truncations
in functional methods, as they provide hints on necessary properties to be
retained in truncations.
