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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Haploid Algebras in C∗ -Tensor Categories and the Schellekens List
AU - Carpi, S.
AU - Gaudio, T.
AU - Giorgetti, L.
AU - Hillier, R.
PY - 2023/8/31
Y1 - 2023/8/31
N2 - We prove that a haploid associative algebra in a C∗-tensor category C is equivalent to a Q-system (a special C∗-Frobenius algebra) in C if and only if it is rigid. This allows us to prove the unitarity of all the 70 strongly rational holomorphic vertex operator algebras with central charge c=24 and non-zero weight-one subspace, corresponding to entries 1–70 of the so called Schellekens list. Furthermore, using the recent generalized deep hole construction of these vertex operator algebras, we prove that they are also strongly local in the sense of Carpi, Kawahigashi, Longo and Weiner and consequently we obtain some new holomorphic conformal nets associated to the entries of the list. Finally, we completely classify the simple CFT type vertex operator superalgebra extensions of the unitary N=1 and N=2 super-Virasoro vertex operator superalgebras with central charge c
AB - We prove that a haploid associative algebra in a C∗-tensor category C is equivalent to a Q-system (a special C∗-Frobenius algebra) in C if and only if it is rigid. This allows us to prove the unitarity of all the 70 strongly rational holomorphic vertex operator algebras with central charge c=24 and non-zero weight-one subspace, corresponding to entries 1–70 of the so called Schellekens list. Furthermore, using the recent generalized deep hole construction of these vertex operator algebras, we prove that they are also strongly local in the sense of Carpi, Kawahigashi, Longo and Weiner and consequently we obtain some new holomorphic conformal nets associated to the entries of the list. Finally, we completely classify the simple CFT type vertex operator superalgebra extensions of the unitary N=1 and N=2 super-Virasoro vertex operator superalgebras with central charge c
U2 - 10.1007/s00220-023-04722-9
DO - 10.1007/s00220-023-04722-9
M3 - Journal article
VL - 402
SP - 169
EP - 212
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 1
ER -