Jones-Wassermann subfactors for modular tensor categories

Zhengwei Liu Feng Xu

Spectral Theory and Operator Algebra mathscidoc:1912.431048

Advances in Mathematics, 355, 106775, 2019.10
The representation category of a conformal net is a unitary modular tensor category. We investigate the reconstruction program: whether all unitary modular tensor categories are representation categories of conformal nets. We give positive evidence: the fruitful theory of multi-interval Jones-Wassermann subfactors on conformal nets is also true for modular tensor categories. We construct multi-interval Jones-Wassermann subfactors for unitary modular tensor categories. We prove that these subfactors are symmetrically self-dual. It generalizes and categorifies the self-duality of finite abelian groups. We call this duality the modular self-duality, because the modularity of the modular tensor category appears in a crucial way. For each unitary modular tensor category, we obtain a sequence of unitary fusion categories. The cyclic group case gives examples of Tambara-Yamagami categories.
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  title={Jones-Wassermann subfactors for modular tensor categories},
  author={Zhengwei Liu, and Feng Xu},
  booktitle={Advances in Mathematics},
Zhengwei Liu, and Feng Xu. Jones-Wassermann subfactors for modular tensor categories. 2019. Vol. 355. In Advances in Mathematics. pp.106775.
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