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arXiv · 2412.12702

Alterfold Theory and Topological Modular Invariance

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

We propose a topological paradigm in alterfold topological quantum field theory to explore various concepts, including modular invariants, $\alpha$-induction and connections in Morita contexts within a modular fusion category of non-zero global dimension over an arbitrary field. Using our topological perspective, we provide streamlined quick proofs and broad generalizations of a wide range of results. These include all theoretical findings by B\"{o}ckenhauer, Evans, and Kawahigashi on $\alpha$-induction. Additionally, we introduce the concept of double $\alpha$-induction for pairs of Morita contexts and define its higher-genus $Z$-transformation, which remains invariant under the action of the mapping class group. Finally, we establish a novel integral identity for modular invariance across multiple Morita contexts, unifying several known identities as special cases.

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BibTeXRIS

Zhengwei Liu, Shuang Ming, Yilong Wang, Jinsong Wu. 2024-12-17. Alterfold Theory and Topological Modular Invariance. https://arxiv.org/abs/2412.12702

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