Modular Invariants, Graphs and $\alpha$-Induction for Nets of Subfactors I
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/9801171,
title = {Modular Invariants, Graphs and $\alpha$-Induction for Nets of Subfactors I},
author = {J. Böckenhauer and D. E. Evans},
journal= {arXiv preprint arXiv:hep-th/9801171},
year = {2009}
}
Comments
36 pages, latex, several corrections, a strong additivity assumption had to be added