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arXiv · 1207.2398

N=2 superconformal nets

Sebastiano Carpi·Robin Hillier·Yasuyuki Kawahigashi·Roberto Longo·Feng Xu
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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.

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BibTeXRIS

Sebastiano Carpi, Robin Hillier, Yasuyuki Kawahigashi, Roberto Longo, Feng Xu. 2014-11-21. N=2 superconformal nets. https://doi.org/10.1007/s00220-014-2234-3

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