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
Carpi, S., Hillier, R., Kawahigashi, Y., Longo, R. (2010). Spectral triples and the super-Virasoro algebra. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 295(1), 71-97 [10.1007/s00220-009-0982-2].
Spectral triples and the super-Virasoro algebra
Carpi, S;LONGO, ROBERTO
2010-01-01
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 superderivationFile | Dimensione | Formato | |
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