New order parameters for non-abelian gauge theories

In recent work a new order parameter has been constructed for abelian gauge theories in the presence of matter, both in the continuum and on the lattice. The order parameter directly probes whether charge is screened and enables the various Higgs phases to be distinguished. We generalize this to non-abelian gauge groups on the lattice, and analyze a specific model of an S₃ gauge theory with S₃ matter. In the course of our general investigation we construct a lattice operator that measures non-abelian discrete charge, and is related to a non-abelian generalization of the 't Hooft loop operator. This also provides further confirmation of the recent prediction that black holes should be able to carry discrete non-abelian quantum hair.