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arXiv · 2206.04570

Equivalence of field theories: Crane-Yetter and the shadow

Jin-Cheng Guu
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Abstract

This work solves a 28-year conjecture by showing that two major invariants of smooth 4-manifolds, the shadow model (motivated by statistical mechanics [Tur91]) and the simplicial Crane-Yetter model (motivated by topological quantum field theory [CY93]), are in fact equal. These invariants, both of which degenerate to the 3D Witten-Reshetikhin-Turaev model in a special case, had been open for years to clarify their relationship. Despite the seeming difference in their origins and formal constructions, we prove their equivalence. Along the way, we sketch a dictionary between the two models, provide a brief survey of the shadow construction \`a la Turaev, and suggest once again that the semisimple models have reached their limits.

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Jin-Cheng Guu. 2022-06-09. Equivalence of field theories: Crane-Yetter and the shadow. https://doi.org/10.1142/s0218216524500366

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