From modular invariants to graphs: the modular splitting method

E. Isasi (1, 2, 3) , Gil Schieber (4, 5)

1 CPT - Centre de Physique Théorique - UMR 6207
2 Departamento de Física
3 CPT - Centre de Physique Théorique - UMR 7332
4 CBPF - Centro Brasileiro de Pesquisas Físicas
5 LPTP - Laboratoire de Physique Théorique et des Particules

We start with a given modular invariant M of a two dimensional su(n)_k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction, 1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; 2) the quantum symmetries of the higher ADE graph G associated to the initial modular invariant M. Notice that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyze several su(3)_k exceptional cases at levels 5 and 9.

Mots clés: conformal field theory; modular invariance; higher ADE systems; fusion algebra; Hopf algebra; quantum groupoids

Domaines: Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]; Algèbres quantiques [math.QA]

E. Isasi, Gil Schieber. From modular invariants to graphs: the modular splitting method. Journal of Physics A: Mathematical and Theoretical, 2007, 40, p. 6513-6537, http://stacks.iop.org/1751-8121/40/6513. ⟨hal-00098045v2⟩