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On Triality Defects in 2d CFT

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arxiv 2208.06077 v4 pith:NTZT5DM3 submitted 2022-08-12 hep-th

Da-Chuan Lu , Zhengdi Sun This is my paper · ORCID
classification hep-th
keywords fusioncategoryciterulecategoriesdifferentgrouprules
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abstract

We consider the triality fusion category discovered in the $c = 1$ KT theory \cite{Thorngren:2021yso}. We analyze this fusion category using the tools from the group theoretical fusion category and describe how to compute the simple lines, fusion rules and $F$-symbols. We then study the physical implication of this fusion category including deriving the spin selection rule, computing the asymptotic density of states of irreps of the fusion category symmetries, and analyzing its anomaly and constraints on the renormalization group flow. There is another set of $F$-symbols for the fusion categories with the same fusion rule known in the literature \cite{teo2015theory} which we compare with, and find the two are different as they lead to different spin selection rules. This gives a complete list of the fusion categories with the same fusion rule by the classification result in \cite{jordan2009classification}.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Non-Local Conserved Currents and Continuous Non-Invertible Symmetries

    hep-th 2025-07 conditional novelty 7.0 of 10

    Non-local conserved currents attached to topological lines generate continuous non-invertible symmetries in 1+1d CFTs, with new examples in SU(2)_k WZW and minimal model products.

  2. Non-Invertible Symmetries in 6d from Green-Schwarz Automorphisms

    hep-th 2024-11 conditional novelty 7.0 of 10

    Non-invertible S3-ality defects are constructed in the 6d (2,0) so(8) SCFT, with fusion rules computed by half-space gauging and SymTFT.

  3. Non-invertible translation from Lieb-Schultz-Mattis anomaly

    cond-mat.str-el 2026-01 conditional novelty 6.0 of 10

    Gauging the full internal symmetry of a lattice system with an LSM anomaly turns lattice translation into a non-invertible operator whose fusion rules involve condensation defects.

  4. SymSETs and self-dualities under gauging non-invertible symmetries

    hep-th 2025-01 conditional novelty 6.0 of 10

    A new SymSET-based construction shows that changing symmetry fractionalization classes can change fusion rules of self-duality defects under non-invertible gauging, yielding new fusion categories such as Rep D16 and Rep SD16.

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