State integral models and the tetrahedron equation
arXiv:2603.09230 · doi:10.1088/1751-8121/ae848f
summary
The paper proves that for a class of state integral models on shaped pseudo‑3‑manifolds, the Boltzmann weight assigned to a tetrahedron satisfies the tetrahedron equation, with the tetrahedron’s dihedral angles serving as spectral parameters.
Abstract
It is shown that for a class of state integral models on shaped pseudo 3-manifolds, including the edge formulation of Teichmüller TQFT, the Boltzmann weight assigned to a tetrahedron solves the tetrahedron equation. The dihedral angles of the tetrahedron play the role of spectral parameters.
15 pages. Published version
Topics & keywords
#state integral models#tetrahedron equation#topological quantum field theory#teichmüller theory#spectral parametersBoltzmann weightpseudo 3-manifolddihedral anglesTeichmüller TQFTtetrahedron equation