  In quantum chromodynamics (QCD), the vacuum structures are taken to be formed
by nonperturbative interactions between gluons. The contributions of gluonic
interactions can be parametrized by gluon condensates and especially the
dimension-2 condensate $\langle A_{\mu}^{2} \rangle$ can be used to generalize
the $\theta$ vacuum. In the generalized picture, each gauge fixed slice forms a
curved surface around a hadron and other strongly interacting objects, and the
propagation of a gluon has to be considered on this curved surface. The gluon
propagator turns out to be massive due to the curvature of the gauge fixed
surface implementing the possibility that the massless gauge bosons might
provide the majority of the hadronic mass and even behave as dark matter in
cosmological scales.
