Order parameters in a modified lattice gauge theory

Mack and Petkova, and Yaffe have recently considered a modified lattice gauge theory, in which the 't Hooft operator has an unexpected area law and is not complementary to the Wilson loop operator. We find that this occurs because the modified theory has a conserved flux not present in the usual lattice theory; as a result, it has two pairs of dual order parameters rather than one. The 't Hooft operator, which probes the physics of interest in the weak-coupling, continuum limit, and which is complementary to the Wilson operator, is not the one considered by the earlier authors. We discuss the order parameters at weak and strong coupling, the corresponding topological fluxes, and the implications for other (lattice or continuum) gauge theories.