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Construction of two-dimensional topological field theories with non-invertible symmetries
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Construction of two-dimensional topological field theories with non-invertible symmetries
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Journal Article
Construction of two-dimensional topological field theories with non-invertible symmetries
2021
Overview
A
bstract
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 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.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V,Springer Nature,SpringerOpen
