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Spectral triples and the super-Virasoro algebra

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<mark>Journal publication date</mark>04/2010
<mark>Journal</mark>Communications in Mathematical Physics
Issue number1
Volume295
Number of pages27
Pages (from-to)71-97
Publication StatusPublished
<mark>Original language</mark>English

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 θ-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 θ-summable generalised spectral triples where there is no Dirac operator but only a superderivation.