State integral models and the tetrahedron equation
Junya Yagi
TL;DR
This paper demonstrates that certain state integral models, including the edge formulation of Teichmüller TQFT, have Boltzmann weights satisfying the tetrahedron equation, with dihedral angles acting as spectral parameters.
Contribution
It establishes a connection between state integral models on pseudo 3-manifolds and solutions to the tetrahedron equation, highlighting the role of dihedral angles as spectral parameters.
Findings
Boltzmann weights solve the tetrahedron equation
Dihedral angles serve as spectral parameters
Includes the edge formulation of Teichmüller TQFT
Abstract
It is shown that for a class of state integral models on shaped pseudo 3-manifolds, including the edge formulation of Teichm\"uller TQFT, the Boltzmann weight assigned to a tetrahedron solves the tetrahedron equation. The dihedral angles of the tetrahedron play the role of spectral parameters.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSpectral Theory in Mathematical Physics · Quantum chaos and dynamical systems · Geometric and Algebraic Topology