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Communications in Mathematical Physics

, Volume 295, Issue 1, pp 71–97 | Cite as

Spectral Triples and the Super-Virasoro Algebra

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

Abstract

We construct infinite dimensional spectral triples associated with representations of the super-Virasoro algebra. In particular the irreducible, unitary positive energy representation of the Ramond algebra with central charge c and minimal lowest weight h = c/24 is graded and gives rise to a net of even θ-summable spectral triples with non-zero Fredholm index. The irreducible unitary positive energy representations of the Neveu-Schwarz algebra give rise to nets of even θ-summable generalised spectral triples where there is no Dirac operator but only a superderivation.

Keywords

Dirac Operator Conformal Field Theory Selfadjoint Operator Spectral Triple Fredholm Module 
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 2010

Authors and Affiliations

  • Sebastiano Carpi
    • 1
  • Robin Hillier
    • 2
  • Yasuyuki Kawahigashi
    • 3
  • Roberto Longo
    • 2
    Email author
  1. 1.Dipartimento di ScienzeUniversità di Chieti-Pescara “G. d’Annunzio”PescaraItaly
  2. 2.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  3. 3.Department of Mathematical SciencesUniversity of TokyoKomaba, TokyoJapan

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