# Spectral triples and the super-Virasoro algebra

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