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

Ziyun Xu

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

Operator Algebras 2025-02-18 v3 Mathematical Physics math.MP

Authors: Ziyun Xu

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.

Keywords

graded local conformal nets $\alpha$-induction braided subfactors superconformal nets classification

Cite

@article{arxiv.2407.01591,
  title  = {The $\alpha$-induction of Graded Local Conformal Nets},
  author = {Ziyun Xu},
  journal= {arXiv preprint arXiv:2407.01591},
  year   = {2025}
}

Comments

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

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

Abstract

Keywords

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