Solving the tetrahedron equation by Teichm\"uller TQFT
Mathematical Physics
2026-02-26 v1 High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
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.
Cite
@article{arxiv.2602.22060,
title = {Solving the tetrahedron equation by Teichm\"uller TQFT},
author = {Myungbo Shim and Xiaoyue Sun and Hao Ellery Wang and Junya Yagi},
journal= {arXiv preprint arXiv:2602.22060},
year = {2026}
}
Comments
18 pages, 9 figures