Research output: Contribution to Journal/Magazine › Journal article › peer-review
Spectral triples and the super-Virasoro algebra. / Carpi, Sebastiano; Hillier, Robin; Kawahigashi, Yasuyuki et al.
In: Communications in Mathematical Physics, Vol. 295, No. 1, 04.2010, p. 71-97.Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Spectral triples and the super-Virasoro algebra
AU - Carpi, Sebastiano
AU - Hillier, Robin
AU - Kawahigashi, Yasuyuki
AU - Longo, Roberto
PY - 2010/4
Y1 - 2010/4
N2 - 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.
AB - 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.
U2 - 10.1007/s00220-009-0982-2
DO - 10.1007/s00220-009-0982-2
M3 - Journal article
VL - 295
SP - 71
EP - 97
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 1
ER -