2023/04/03 by Zhang, Carolyn, Córdova, Clay · 3 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2304.01262
We present a general approach for detecting when a fusion category symmetry is anomalous, based on the existence of a special kind of Lagrangian algebra of the corresponding Drinfeld center. The Drinfeld center of a fusion category A describes a (2+1)D topological order whose gapped boundaries enumerate all (1+1)D gapped phases with the fusion category symmetry, which may be spontaneously broken. There always exists a gapped boundary, given by the electric Lagrangian algebra, that describes a phase with A fully spontaneously broken. The symmetry defects of this boundary can be identified with the objects in A. We observe that if there exists a different gapped boundary, given by a magnetic Lagrangian algebra, then there exists a gapped phase where A is not spontaneously broken at all, which means that A is not anomalous. In certain cases, we show that requiring the existence of such a magnetic Lagrangian algebra leads to highly computable obstructions to A being anomaly-free. As an application, we consider the Drinfeld centers of ℤN×ℤN Tambara-Yamagami fusion categories and recover known results from the study of fiber functors.