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

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.

arXiv comment39 pages, tikz figures

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• Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory
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