Liquid crystal defects and confinement in Yang-Mills theory

We show that in the Landau gauge of the $SU(2)$ Yang-Mills theory the residual global symmetry supports existence of the topological vortices which resemble disclination defects in the nematic liquid crystals and the Alice (half-quantum) vortices in the superfluid $\mathrm{^3He}$ in the A-phase. The theory also possesses half-integer and integer-charged monopoles which are analogous to the point-like defects in the nematic crystal and in the liquid helium. We argue that the deconfinement phase transition in the Yang-Mills theory in the Landau gauge is associated with the proliferation of these vortices and/or monopoles.