  We study possibilities to define a static quark anti-quark pair in a
colour-adjoint orientation based on Wilson loops with generator insertions,
using both lattice QCD and leading order perturbation theory in various gauges.
Non-perturbatively, the only way to obtain non-zero results while maintaining
positivity of the Hamiltonian is by some form of temporal gauge. In this case
the correlator is equivalent to a gauge invariant correlation function of a
static quark anti-quark pair and a static adjoint quark, the resulting
three-point potential is attractive. Saturating open colour indices with colour
magnetic fields instead also leads to a gauge invariant correlator. However
this object is found to couple to the singlet sector only. There appears to be
no lattice observable that reproduces the repulsive adjoint potential predicted
by perturbation theory in Lorenz or Coulomb gauges.
