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

Journal of High Energy Physics

Ying-Hsuan Lin¹  Sahand Seifnashri²  Tzu-Chen Huang³ 

[1] Jefferson Physical Laboratory, Harvard University;Simons Center for Geometry and Physics, Stony Brook University;Walter Burke Institute for Theoretical Physics, California Institute of Technology;

关键词: Topological Field Theories;    Discrete Symmetries;    Global Symmetries;    Anomalies in Field and String Theories;   

DOI  :  10.1007/JHEP12(2021)028

来源: DOAJ

【 摘 要 】

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 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.

【 授权许可】

Unknown