# $N=2$ superconformal nets

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.

Keywords:

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