Characterization and Classification of Fermionic Symmetry Enriched Topological Phases

Understand

We examine the interplay of symmetry and topological order in $2+1$ dimensional fermionic topological phases of matter.

• We define fermionic topological symmetries acting on the emergent topological effective theory described using braided tensor category theory.
• Connecting this to the ${\cal G}^{\rm f}$ fermionic symmetry of the microscopic physical system, we characterize and classify symmetry fractionalization in fermionic topological phases.
• We find that the physical fermion provides constraints that result in a tiered structure of obstructions and classification of fractionalization with respect to the physical fermions, the quasiparticles, and the vortices.