Fractionalizing Global Symmetry on Looplike Topological Excitations

Understand

Symmetry fractionalization (SF) on topological excitations is one of the most remarkable quantum phenomena in topological orders with symmetry, i.e., symmetry-enriched topological phases.

• While much progress has been theoretically and experimentally made in 2D, the understanding on SF in 3D is far from complete.
• A long-standing challenge is to understand SF on looplike topological excitations which are spatially extended objects.
• In this work, we construct a powerful topological-field-theoretical framework approach for 3D topological orders, which leads to a systematic characterization and classification of SF.