Reconstructing CFTs from TQFTs

MATHEMATICAL PICTURE LANGUAGE

Speaker:

Zhenghan Wang - Microsoft and UCSB

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 

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