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Relative Anomalies in (2+1)D Symmetry Enriched Topological States · Around

2019

Relative Anomalies in (2+1)D Symmetry Enriched Topological States

Barkeshli, Maissam, Cheng, Meng

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Certain patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state.

An important question is to determine how to compute this anomaly, which means determining which SPT hosts a given symmetry-enriched topological order at its surface.
While special cases are known, a general method to compute the anomaly has so far been lacking.
In this paper we propose a general method to compute relative anomalies between different symmetry fractionalization classes of a given (2+1)D topological order.

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