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Spectral triples and the super-Virasoro algebra · Around

2008

Spectral triples and the super-Virasoro algebra

Carpi, Sebastiano, Hillier, Robin, Kawahigashi, Yasuyuki et al.

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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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