Solving the tetrahedron equation by Teichm\"uller TQFT
classification
🧮 math-ph
hep-thmath.MPnlin.SI
keywords
modelsequationteichmtetrahedrontqftullerapproachassumptions
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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 Teichm\"uller TQFT.
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Cited by 1 Pith paper
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Tetrahedral $L$-operators, tensor Schur polynomials and $q$-deformed loop elementary symmetric functions
Tetrahedral L-operator partition functions equal tensor Schur polynomials when q=0 and q-deformed loop elementary symmetric functions in general.
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