The $\alpha$-induction of Graded Local Conformal Nets

Abstract

The $\alpha$-induction of graded local conformal nets is studied. We show that inclusions of graded local conformal nets give rise to braided subfactors so that the $\alpha$-induction is still effective for graded local conformal nets. As an application, we give a shorter proof of classification of $N=2$ superconformal nets in the discrete series.

The notion of graded localized endomorphisms is included. Some essential information missing in the previous version is added. arXiv admin note: substantial text overlap with arXiv:1207.2398, arXiv:1304.4062 by other authors