Demonstrates lattice model construction in 3-manifolds, indicating integrability via Teichmüller TQFT.
A bstract We propose an approach to construct three-dimensional lattice models using line defects in state integral models on shaped triangulations of 3-manifolds. The Boltzmann weights for these models satisfy a variant of the tetrahedron equation, which implies integrability under suitable assumptions on R-matrices and transfer matrices. As an explicit example, we present a solution produced by Teichmüller TQFT.
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Shim et al. (2026) studied this question.
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