Modular Invariants, Graphs and $α$-Induction for Nets of Subfactors II

Details Modular Invariants, Graphs and $α$-Induction for Nets of Subfactors II Modular Invariants, Graphs and $α$-Induction for Nets of Subfactors II

1998-05-05

arxiv.org/abs/hep-th/9805023v1

Commun.Math.Phys. 200 (1999) 57-103

Physics

High Energy Physics

High Energy Physics - Theory

63 pages, latex2e

Scientific paper

10.1007/s002200050523

We apply the theory of $\alpha$-induction of sectors which we elaborated in our previous paper to several nets of subfactors arising from conformal field theory. The main application are conformal embeddings and orbifold inclusions of SU(n) WZW models. For the latter, we construct the extended net of factors by hand. Developing further some ideas of F. Xu, our treatment leads canonically to certain fusion graphs, and in all our examples we rediscover the graphs Di Francesco, Petkova and Zuber associated empirically to the corresponding SU(n) modular invariants. We establish a connection between exponents of these graphs and the appearance of characters in the block-diagonal modular invariants, provided that the extended modular S-matrices diagonalize the endomorphism fusion rules of the extended theories. This is proven for many cases, and our results cover all the block-diagonal SU(2) modular invariants, thus provide some explanation of the A-D-E classification.

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