Generalized symmetries

The concept of symmetry has been generalized in the past decade, and how to utilize these powerful tools is still under exploration.

Higher-form symmetry is one such generalization, extending charged objects from local field operators to extended objects, such as Wilson lines in 1-form symmetry. It has been proposed that the vacuum expectation value of a Wilson loop can serve as an order parameter to distinguish different phases.

On the other hand, condensed matter physicists have known for decades that certain rare-earth materials share the pyrochlore lattice structure, and that electromagnetism can emerge at low energies.

It is of great interest to understand this phenomenon in light of the recent advances in generalized symmetry, and to use the Wilson loop as a topological quantity to characterize the phase transition.