The many faces of Ocneanu cells

Details The many faces of Ocneanu cells The many faces of Ocneanu cells

2001-01-23

arxiv.org/abs/hep-th/0101151v3

Nucl.Phys. B603 (2001) 449-496

Physics

High Energy Physics

High Energy Physics - Theory

57 pages, 10 figures. Several misprints and the derivation of eq. (7.38) corrected

Scientific paper

10.1016/S0550-3213(01)00096-7

We define generalised chiral vertex operators covariant under the Ocneanu ``double triangle algebra'' {\cal A}, a novel quantum symmetry intrinsic to a given rational 2-d conformal field theory. This provides a chiral approach, which, unlike the conventional one, makes explicit various algebraic structures encountered previously in the study of these theories and of the associated critical lattice models, and thus allows their unified treatment. The triangular Ocneanu cells, the 3j-symbols of the weak Hopf algebra {\cal A}, reappear in several guises. With {\cal A} and its dual algebra {hat A} one associates a pair of graphs, G and {\tilde G}. While G are known to encode complete sets of conformal boundary states, the Ocneanu graphs {\tilde G} classify twisted torus partition functions. The fusion algebra of the twist operators provides the data determining {\hat A}. The study of bulk field correlators in the presence of twists reveals that the Ocneanu graph quantum symmetry gives also an information on the field operator algebra.

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