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DTSTART;TZID=America/New_York:20230512T100000
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DTSTAMP:20260526T004340
CREATED:20230802T171128Z
LAST-MODIFIED:20240215T111609Z
UID:10001179-1683885600-1683891000@cmsa.fas.harvard.edu
SUMMARY:Anomalies of (1+1)D categorical symmetries
DESCRIPTION:Quantum Matter Seminar \nSpeaker: Carolyn Zhang (U Chicago) \nTitle: Anomalies of (1+1)D categorical symmetries \nAbstract: 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 \emph{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 \emph{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 $\mathbb{Z}_N\times\mathbb{Z}_N$ Tambara-Yamagami fusion categories and recover known results from the study of fiber functors.
URL:https://cmsa.fas.harvard.edu/event/qm_51223/
LOCATION:Virtual
CATEGORIES:Quantum Matter
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