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Construction of two-dimensional topological field theories with non-invertible symmetries

Tzu-Chen Huang Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, U.S.A. Ying-Hsuan Lin Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, U.S.A. Sahand Seifnashri Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY 11794-3636, U.S.A.; C.N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY 11794-3840, U.S.A.

arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2203.74002

Journal of High Energy Physics, (28), 2021.7
We construct the defining data of two-dimensional topological field theories (TFTs) enriched by non-invertible symmetries/topological defect lines. Simple formulae for the three-point functions and the lasso two-point functions are derived, and crossing symmetry is proven. The key ingredients are open-to-closed maps and a boundary crossing relation, by which we show that a diagonal basis exists in the defect Hilbert spaces. We then introduce regular TFTs, provide their explicit constructions for the Fibonacci, Ising and Haagerup ℋ3 fusion categories, and match our formulae with previous bootstrap results. We end by explaining how non-regular TFTs are obtained from regular TFTs via generalized gauging.
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@inproceedings{tzu-chen2021construction,
  title={Construction of two-dimensional topological field theories with non-invertible symmetries},
  author={Tzu-Chen Huang, Ying-Hsuan Lin, and Sahand Seifnashri},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220317171434251735005},
  booktitle={Journal of High Energy Physics},
  number={28},
  year={2021},
}
Tzu-Chen Huang, Ying-Hsuan Lin, and Sahand Seifnashri. Construction of two-dimensional topological field theories with non-invertible symmetries. 2021. In Journal of High Energy Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220317171434251735005.
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