  Instanton-dyons, also known as instanton-monopoles or instanton-quarks, are
topological constituents of the instantons at nonzero temperature and nonzero
expectation value of $A_4$. While the interaction between instanton-dyons has
been calculated to one-loop order by a number of authors, that for
dyon-antidyon pairs remains unknown even at the classical level. In this work
we are filling this gap, by solving the gradient flow equation on a 3d lattice.
We start with two well separated objects. We find that, after initial rapid
relaxation, the configurations follow "streamline" set of configurations, which
is basically independent on the initial configurations used. In striking
difference to instanton-antiinstanton streamlines, in this case it ends at a
quasi-stationary configuration, with an abrupt drop to perturbative fields. We
parameterize the action of the streamline configurations, which is to be used
in future many-body calculations.
