Spectral triples and the super-Virasoro algebra
Operator Algebras
2010-02-11 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Quantum Algebra
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 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.
Cite
@article{arxiv.0811.4128,
title = {Spectral triples and the super-Virasoro algebra},
author = {Sebastiano Carpi and Robin Hillier and Yasuyuki Kawahigashi and Roberto Longo},
journal= {arXiv preprint arXiv:0811.4128},
year = {2010}
}
Comments
27 pages; v2: a comment concerning the difficulty in defining cyclic cocycles in the NS case have been added