Folding approach to topological order enriched by mirror symmetry

Understanding the role of global symmetries and their quantum anomalies in two-dimensional topological order is a challenging problem, especially for time-reversal and mirror-reflection symmetries. Here, the authors develop a new folding approach to mirror-symmetry enriched topological order, which relates this problem to anyon-condensation theory. The approach is physically transparent and easy to compute for some simple, yet important examples. The folding approach can be generalized to study topological order with many other crystalline symmetries and their quantum anomalies.