Spectral triples and the super-Virasoro algebra

Details Spectral triples and the super-Virasoro algebra Spectral triples and the super-Virasoro algebra

2008-11-25

arxiv.org/abs/0811.4128v2

Commun.Math.Phys.295:71-97,2010

Mathematics

Operator Algebras

27 pages; v2: a comment concerning the difficulty in defining cyclic cocycles in the NS case have been added

Scientific paper

10.1007/s00220-009-0982-2

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.

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