Spectral triples and the super-Virasoro algebra

Sebastiano Carpi, Robin Hillier, Yasuyuki Kawahigashi, Roberto Longo
November 25, 2008
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 theta-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 theta-summable generalised spectral triples where there is no Dirac operator but only a superderivation.
open access link Commun.Math.Phys.295:71-97,2010
@article{Carpi:2008jm, author = "Carpi, Sebastiano and Hillier, Robin and Kawahigashi, Yasuyuki and Longo, Roberto", title = "{Spectral triples and the super-Virasoro algebra}", journal = "Commun. Math. Phys.", volume = "295", year = "2010", pages = "71-97", doi = "10.1007/s00220-009-0982-2", eprint = "0811.4128", archivePrefix = "arXiv", primaryClass = "math.OA", SLACcitation = "%%CITATION = ARXIV:0811.4128;%%" }

Keywords: 
spectral triples, super-Virasoro algebra, Ramond algebra, Neveu-Schwarz algebra