2024/05/28 by Aaron Hofer, Hofer, Aaron, Ingo Runkel +1
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2405.18038
openalex publication_date 2024/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a not necessarily semisimple modular tensor category C, we use the corresponding 3d TFT defined in [arXiv:1912.02063] to explicitly describe a modular functor as a symmetric monoidal 2-functor from a 2-category of oriented bordisms to a 2-category of finite linear categories. This recovers a result by Lyubashenko [arXiv:hep-th/9405168] obtained via generators and relations. Pulling back the modular functor for C to a 2-category of bordisms with orientation reversing involution cancels the gluing anomaly, and further pulling back to the original bordism category along a doubling functor leads to the modular functor for the Drinfeld centre Z(C).