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

• URL: http://arxiv.org/abs/2208.14566v1
• Date: Tue, 30 Aug 2022 23:26:31 GMT
• Title: Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups
• Authors: Nathan Geer, Aaron D. Lauda, Bertrand Patureau-Mirand, and Joshua Sussan
• Abstract summary: We prove that relative Hermitian modular categories give rise to modified Hermitian WRT-TQFTs. The Hermitian theory is applied to define new pseudo-Hermitian topological phases that can be considered as non-semisimple analogs of Levin-Wen models.
• Score: 23.31108679980856
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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