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Communications in Mathematical Physics

, Volume 336, Issue 3, pp 1285–1328 | Cite as

N =2 Superconformal Nets

  • Sebastiano Carpi
  • Robin Hillier
  • Yasuyuki Kawahigashi
  • Roberto LongoEmail author
  • Feng Xu
Article

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.

Keywords

Central Charge Superconformal Algebra Irreducible Unitary Representation Chiral Ring Spectral Triple 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Sebastiano Carpi
    • 1
  • Robin Hillier
    • 2
  • Yasuyuki Kawahigashi
    • 3
    • 4
  • Roberto Longo
    • 5
    Email author
  • Feng Xu
    • 6
  1. 1.Dipartimento di EconomiaUniversità di Chieti-Pescara “G. d’Annunzio”PescaraItaly
  2. 2.Department of Mathematics and StatisticsLancaster UniversityLancasterUK
  3. 3.Department of Mathematical SciencesThe University of TokyoTokyoJapan
  4. 4.Kavli IPMU (WPI)The University of TokyoKashiwaJapan
  5. 5.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  6. 6.Department of MathematicsUniversity of California at RiversideRiversideUSA

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