N = 2 superconformal nets

Carpi, Sebastiano and Hillier, Robin and Kawahigashi, Yasuyuki and Longo, Roberto and Xu, Feng (2015) N = 2 superconformal nets. Communications in Mathematical Physics, 336 (3). pp. 1285-1328. ISSN 0010-3616

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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.

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Communications in Mathematical Physics
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25 Sep 2014 07:32
Last Modified:
16 Sep 2023 00:56