# $N=2$ superconformal nets

July 10, 2012

We provide an operator algebraic approach to $N=2$ chiral conformal field
theory and set up the noncommutative geometric framework. Compared to the $N=1$
case, the structure here is much richer. There are naturally associated nets of
spectral triples and the JLO cocycles separate the Ramond sectors. We construct
the $N=2$ superconformal nets of von Neumann algebras in general, classify them
in the discrete series $c<3$, and study spectral flow. We prove the coset
identification for the $N=2$ super-Virasoro nets with $c<3$, a key result whose
equivalent in the vertex algebra context is seemingly not complete. Finally,
the chiral ring is discussed in terms of net representations.

open access link
Communications in Mathematical Physics 336 (2015), no. 3,
1285-1328

@article{Carpi:2012va,
author = "Carpi, Sebastiano and Hillier, Robin and Kawahigashi,
Yasuyuki and Longo, Roberto and Xu, Feng",
title = "{N =2 Superconformal Nets}",
journal = "Commun. Math. Phys.",
volume = "336",
year = "2015",
pages = "1285-1328",
doi = "10.1007/s00220-014-2234-3",
eprint = "1207.2398",
archivePrefix = "arXiv",
primaryClass = "math.OA",
SLACcitation = "%%CITATION = ARXIV:1207.2398;%%"
}

Keywords:

*none*