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


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.


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