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arXiv · 2406.16700

Anomalies in mirror symmetry enriched topological orders

Zhaoyang Ding·Yang Qi
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Abstract

Two-dimensional mirror symmetry enriched topological (SET) orders can be studied using the folding approach: it can be folded along the mirror axis and turned into a bilayer system on which the mirror symmetry acts as a $\mathbb Z_2$ layer-exchange symmetry. How mirror symmetry enriches the topological order is then encoded at the mirror axis, which is a gapped boundary of the folded bilayer system. Based on anyon-condensation theory, we classify possible $\mathbb Z_2$-symmetric gapped boundaries of the folded system. In particular, we derive an $H^2$ obstruction function, which corresponds to an $H^3$ obstruction for topological orders enriched by the time-reversal symmetry instead of mirror symmetry. We demonstrate that states with a nontrivial $H^2$ obstruction function can be constructed on the surface of a three-dimensional mirror SET order.

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Zhaoyang Ding, Yang Qi. 2024-06-24. Anomalies in mirror symmetry enriched topological orders. https://doi.org/10.1103/physrevb.110.155151

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