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arXiv · 2405.18038

Modular functors from non-semisimple 3d TFTs

Aaron Hofer·Ingo Runkel
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Abstract

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).

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Aaron Hofer, Ingo Runkel. 2024-05-28. Modular functors from non-semisimple 3d TFTs. https://arxiv.org/abs/2405.18038

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