Anomaly-free symmetries with obstructions to gauging and onsiteability

Abstract: Despite the long history of the study of 't Hooft anomalies and their broad applications, there is still a lack of consensus on the precise definition of 't Hooft anomalies. Two common definitions are 1) obstructions to gauging a symmetry and 2) obstructions to a trivially symmetric state. It is often believed that these two definitions are equivalent, and indeed they were recently proven to be equivalent in 1+1D spin chains with finite, internal, unitary symmetries. We show that this is not the case in 2+1D. In particular, we present an index $\omega\in H^2(G,Q^{\times})$ for 0-form finite, internal, unitary symmetries where $Q^{\times}$ is the group of rational numbers under multiplication. We show that symmetries with nontrivial $\omega$ cannot be gauged or made on-site, but nevertheless admit trivially symmetric product states with symmetric commuting parent Hamiltonians.

mathematical physics

Audience: researchers in the discipline

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