N=2 superconformal nets
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 we define and study an operator algebraic version of the N=2 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 has seemingly not been completely proved so far. Finally, the chiral ring is discussed in terms of net representations.
Cite
@article{arxiv.1207.2398,
title = {N=2 superconformal nets},
author = {Sebastiano Carpi and Robin Hillier and Yasuyuki Kawahigashi and Roberto Longo and Feng Xu},
journal= {arXiv preprint arXiv:1207.2398},
year = {2015}
}
Comments
42 pages. Final version to be published in Communications in Mathematical Physics