We develop the categorical context for defining Hermitian non-semisimple topological quantum field theories (TQFTs). We prove that relative Hermitian modular categories give rise to modified Hermitian Witten–Reshetikhin–Turaev 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.

中文翻译：

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量子（超）群的非半简单 Levin-Wen 模型和 Hermitian TQFT

我们开发了用于定义厄米非半简单拓扑量子场论（TQFT）的分类上下文。我们证明相对埃尔米特模范畴产生了修正的埃尔米特维滕-列谢蒂欣-图拉耶夫 TQFT，并提供了来自量子群和量子超代数表示论的这些结构的大量例子。这里为改进的 Turaev-Viro TQFT 开发的埃尔米特理论应用于定义新的伪埃尔米特拓扑相，可以将其视为 Levin-Wen 模型的非半简单类似物。