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arXiv · 2312.06477

Alterfold Topological Quantum Field Theory

Zhengwei Liu·Shuang Ming·Yilong Wang·Jinsong Wu
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Abstract

We introduce the 3-alterfold topological quantum field theory (TQFT) by extending the quantum invariant of 3-alterfolds. The bases of the TQFT are explicitly characterized and the Levin-Wen model is naturally interpreted in 3-alterfold TQFT bases. By naturally considering the RT TQFT and TV TQFT as sub-TQFTs within the 3-alterfold TQFT, we establish their equivalence. The 3-alterfold TQFT is unitary when the input fusion category is unitary. Additionally, we extend the 3-alterfold TQFT to the Morita context and demonstrate that Morita equivalent fusion categories yield equivalent TV TQFTs. We also provide a simple pictorial proof of complete positivity criteria for unitary categorization when the 3-alterfold TQFT is unitary. Expanding our scope to high-genus surfaces by replacing the torus, we introduce the high genus topological indicators and proving the equivariance under the mapping class group actions.

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BibTeXRIS

Zhengwei Liu, Shuang Ming, Yilong Wang, Jinsong Wu. 2023-12-11. Alterfold Topological Quantum Field Theory. https://arxiv.org/abs/2312.06477

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