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N = 2 superconformal nets

Research output: Contribution to journalJournal articlepeer-review

Published
  • Sebastiano Carpi
  • Robin Hillier
  • Yasuyuki Kawahigashi
  • Roberto Longo
  • Feng Xu
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<mark>Journal publication date</mark>06/2015
<mark>Journal</mark>Communications in Mathematical Physics
Issue number3
Volume336
Number of pages44
Pages (from-to)1285-1328
Publication StatusPublished
Early online date27/11/14
<mark>Original language</mark>English

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 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.