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.

### Spectral triples and the super-Virasoro 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11564/135010
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