Tensor networks, fusion categories and operator algebras

Certain 4-tensors have been used to study two-dimensional topological order, and we identified them with bi-unitary connections in subfactor theory of Jones before. This identification gives a description of a fusion category using a (possibly non-flat) bi-unitary connection, which arises as quantum 6j-symbols for a multi-fusion category. We further advance this identification by working on the zipper condition, which is a kind of pentagon equation, and flat fields of strings.

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