Location: Zoom https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

Time: Tuesday, October 6, 2020, 10:00 AM (Eastern US), 15:00 (UK/Eire), 16:00 (Central Europe), 22:00 (China)

Title: Reconstructing CFTs from MTCs

Abstract: Inspired by fractional quantum Hall physics and Tannaka-Krein duality, it is conjectured that every modular tensor category (MTC) or (2+1)-topological quantum field theory (TQFT) can be realized as the representation category of a vertex operator algebra (VOA) or chiral conformal field theory (CFT). It is obviously true for quantum group/WZW MTCs, but it is not known for MTCs appeared in subfactors such as the famous double Haagerup. After some general discussion, I will focus on pointed MTCs or so-called abelian anyon models. While all abelian anyon models can be realized by lattice VOAs, it is not clear whether or not they can be realized by non-lattice VOAs. The trivial MTC is realized by the Monster moonshine module, which is a non-lattice realization. I will provide evidence that this might be true for all abelian anyon models. The talk is partially based on a joint work with Liang Wang: https://arxiv.org/abs/2004.12048

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