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arXiv · 2110.02958

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

Tzu-Chen Huang·Ying-Hsuan Lin·Sahand Seifnashri
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Abstract

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 $\mathcal{H}_3$ 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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Tzu-Chen Huang, Ying-Hsuan Lin, Sahand Seifnashri. 2021-10-06. Construction of two-dimensional topological field theories with non-invertible symmetries. https://doi.org/10.1007/jhep12(2021)028

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