Mirror anomaly in fermionic topological orders

Understand

We study general 2D fermionic topological orders enriched by the mirror symmetry with $\mathcal{M}^2=1$.

• It is known that certain mirror symmetry enriched fermionic topological orders (mirror SETs) are anomalous, in the sense that they cannot be realized in strict two dimensions but have to live on the surface of 3D topological crystalline superconductors.
• Mirror anomaly, or equivalently 3D topological crystalline superconductor, has a $\mathbb{Z}_{16}$ classification.
• In this work, we derive an explicit expression, namely an \emph{anomaly indicator}, for the $\mathbb{Z}_{16}$ mirror anomaly for general fermionic mirror SETs.