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

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

1998-01-26

arxiv.org/abs/hep-th/9801171v2

Commun.Math.Phys. 197 (1998) 361-386

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, latex, several corrections, a strong additivity assumption had to be added

Scientific paper

10.1007/s002200050455

We analyze the induction and restriction of sectors for nets of subfactors defined by Longo and Rehren. Picking a local subfactor we derive a formula which specifies the structure of the induced sectors in terms of the original DHR sectors of the smaller net and canonical endomorphisms. We also obtain a reciprocity formula for induction and restriction of sectors, and we prove a certain homomorphism property of the induction mapping. Developing further some ideas of F. Xu we will apply this theory in a forthcoming paper to nets of subfactors arising from conformal field theory, in particular those coming from conformal embeddings or orbifold inclusions of SU(n) WZW models. This will provide a better understanding of the labeling of modular invariants by certain graphs, in particular of the A-D-E classification of SU(2) modular invariants.

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