Carpi, Sebastiano and Hillier, Robin and Kawahigashi, Yasuyuki and Longo, Roberto and Xu, Feng
(2015)
*N = 2 superconformal nets.*
Communications in Mathematical Physics, 336 (3).
pp. 1285-1328.
ISSN 0010-3616

## Abstract

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.