N=2 Superconformal Nets

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