Anomaly and symmetry fractionalization of mirror-symmetric fermionic topological orders

We study symmetry fractionalization and quantum anomaly in general 2D fermionic topological orders with the mirror reflection symmetry. A set of constraints on mirror fractionalization and an explicit anomaly indicator formula are derived. Our derivation is based on the recently developed folding approach, which was originally proposed in bosonic topological orders. The anomalous mirror-symmetric topological orders can only live on the surface of 3D topological crystalline superconductors, and we establish a direct bulk-boundary correspondence.