1207.2398 (Sebastiano Carpi et al.)

N=2 superconformal nets    [PDF]

Sebastiano Carpi, Robin Hillier, Yasuyuki Kawahigashi, Roberto Longo, Feng Xu

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.

View original: http://arxiv.org/abs/1207.2398