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arXiv · 2208.14566

Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups

Nathan Geer·Aaron D. Lauda·Bertrand Patureau-Mirand·Joshua Sussan
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Abstract

We develop the categorical context for defining Hermitian non-semisimple TQFTs. We prove that relative Hermitian modular categories give rise to modified Hermitian WRT-TQFTs and provide numerous examples of these structures coming from the representation theory of quantum groups and quantum superalgebras. The Hermitian theory developed here for the modified Turaev-Viro TQFT is applied to define new pseudo-Hermitian topological phases that can be considered as non-semisimple analogs of Levin-Wen models.

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BibTeXRIS

Nathan Geer, Aaron D. Lauda, Bertrand Patureau-Mirand, Joshua Sussan. 2022-08-30. Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups. https://doi.org/10.1112/jlms.12853

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