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.
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Communicated by A. Connes
Dedicated to Sergio Doplicher on the occasion of his 70th birthday
Supported in part by PRIN-MIUR, GNAMPA-INDAM and EU network “Noncommutative Geometry” MRTN-CT-2006-0031962.
Supported by the Gottlieb Daimler- und Karl Benz-Stiftung with a one year research scholarship.
Supported in part by the Grants-in-Aid for Scientific Research, JSPS.
Supported in part by the ERC Advanced Grant 227458 OACFT “Operator Algebras and Conformal Field Theory”.
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Carpi, S., Hillier, R., Kawahigashi, Y. et al. Spectral Triples and the Super-Virasoro Algebra. Commun. Math. Phys. 295, 71–97 (2010). https://doi.org/10.1007/s00220-009-0982-2
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DOI: https://doi.org/10.1007/s00220-009-0982-2