Generalized Longo-Rehren Subfactors and α-Induction

Abstract

We study the recent construction of subfactors by Rehren which generalizes the Longo-Rehren subfactors. We prove that if we apply this construction to a non-degenerately braided subfactor N subset M and alpha-induction, then the resulting subfactor is dual to the Longo-Rehren subfactor M tensor M^opp subset R arising from the entire system of irreducible endomorphisms of M resulting from alpha-induction. As a corollary, we solve a problem on existence of braiding raised by Rehren negatively. Furthermore, we generalize our previous study with Longo and Muger on multi-interval subfactors arising from a completely rational conformal net of factors on S^1 to a net of subfactors and show that the (generalized) Longo-Rehren subfactors and alpha-induction naturally appear in this context.