Spectral triples and the super-Virasoro algebra

Carpi, Sebastiano and Hillier, Robin and Kawahigashi, Yasuyuki and Longo, Roberto (2010) Spectral triples and the super-Virasoro algebra. Communications in Mathematical Physics, 295 (1). pp. 71-97. ISSN 0010-3616

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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 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.

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Communications in Mathematical Physics
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17 Jun 2013 11:17
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21 Nov 2022 23:56