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

TL;DR

This paper explores the $eta$-induction process for graded local conformal nets, demonstrating its effectiveness in producing braided subfactors and providing a streamlined proof for classifying $N=2$ superconformal nets.

Contribution

It extends the $eta$-induction framework to graded local conformal nets and applies it to simplify the classification of $N=2$ superconformal nets.

Findings

$eta$-induction yields braided subfactors for graded nets

Shorter proof for $N=2$ superconformal net classification

Validation of $eta$-induction's effectiveness in graded contexts

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.