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Alterfold Topological Quantum Field Theory

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arxiv 2312.06477 v1 pith:BWQOWUIG submitted 2023-12-11 math-ph math.CTmath.MPmath.OAmath.QA

Zhengwei Liu , Shuang Ming , Yilong Wang , Jinsong Wu This is my paper · ORCID
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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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Cited by 2 Pith papers

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  1. Generalizations of Frobenius-Schur indicators from Kuperberg invariants

    math.QA 2025-06 conditional novelty 7.0 of 10

    Kuperberg invariants of framed lens spaces and a genus-2 family are gauge invariants of finite-dimensional Hopf algebras, generalizing Frobenius-Schur indicators.

  2. A 2D-CFT Factory: Critical Lattice Models from Competing Anyon Condensation Processes in SymTO/SymTFT

    cond-mat.str-el 2025-06 conditional novelty 7.0 of 10

    Competing anyon condensates in string-net models generate critical lattice models, including new Haagerup-symmetric CFT candidates with central charges near 1.3, 1.8 and 2.5.

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