Notes on TQFT Wire Models and Coherence Equations for SU(3) Triangular Cells
Robert Coquereaux, Esteban Isasi, Gil Schieber
TL;DR
This paper explores the connection between TQFT wire models, Kuperberg equations, and Ocneanu coherence equations for SU(3), providing solutions and insights into the structure of fusion categories at various levels.
Contribution
It establishes a link between Kuperberg equations and Ocneanu coherence equations for SU(3), offering methods to solve these equations in specific cases.
Findings
Derived solutions for Ocneanu coherence equations in several examples
Connected TQFT wire models with fusion graph modules for SU(3)
Enhanced understanding of triangular cell systems in fusion categories
Abstract
After a summary of the TQFT wire model formalism we bridge the gap from Kuperberg equations for SU(3) spiders to Ocneanu coherence equations for systems of triangular cells on fusion graphs that describe modules associated with the fusion category of SU(3) at level k. We show how to solve these equations in a number of examples.
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