$N=2$ superconformal nets

Sebastiano Carpi, Robin Hillier, Yasuyuki Kawahigashi, Roberto Longo, Feng Xu
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;%%" }