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

Huang, Tzu-Chen and Lin, Ying-Hsuan and Seifnashri, Sahand (2021) Construction of two-dimensional topological field theories with non-invertible symmetries. Journal of High Energy Physics, 2021 (12). Art. No. 28. ISSN 1126-6708. doi:10.1007/JHEP12(2021)028.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Huang, Tzu-Chen0000-0002-8738-7695
Lin, Ying-Hsuan0000-0001-8904-1287
Seifnashri, Sahand0000-0001-5217-0587
Additional Information:© 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: November 1, 2021; Accepted: November 23, 2021; Published: December 7, 2021. We are grateful to Kantaro Ohmori and Yuji Tachikawa for facilitating this collaboration, and to Yifan Wang for helpful discussions. We also thank Zohar Komargodski, Kantaro Ohmori, Shu-Heng Shao, Yuji Tachikawa, and Yifan Wang for comments on the first draft. YL thanks Noah Snyder and SS thanks Jin-Cheng Guu for consultation on the Frobenius-Schur indicator. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DESC0011632. YL is supported by the Simons Collaboration Grant on the Non-Perturbative Bootstrap. SS is also supported in part by the Simons Foundation grant 488657 (Simons Collaboration on the Non-Perturbative Bootstrap).
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons Foundation488657
Subject Keywords:Topological Field Theories, Discrete Symmetries, Global Symmetries, Anomalies in Field and String Theories
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Issue or Number:12
Record Number:CaltechAUTHORS:20211018-224858534
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Official Citation:Huang, TC., Lin, YH. & Seifnashri, S. Construction of two-dimensional topological field theories with non-invertible symmetries. J. High Energ. Phys. 2021, 28 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111540
Deposited By: Joy Painter
Deposited On:18 Oct 2021 23:38
Last Modified:14 Dec 2021 16:54

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