On the symmetry of odd Leech lattice CFT
Abstract We show that the Mathieu groups M 24 and M 23 in the isometry group of the odd Leech lattice do not lift to subgroups of the automorphism group of its lattice vertex operator (super)algebra. In other words, the subgroups 224.M 24 and 223.M 23 of the automorphism group of the odd Leech latti...
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| Language: | English |
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2025-06-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP06(2025)208 |
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| author | Masaki Okada |
| author_facet | Masaki Okada |
| author_sort | Masaki Okada |
| collection | DOAJ |
| description | Abstract We show that the Mathieu groups M 24 and M 23 in the isometry group of the odd Leech lattice do not lift to subgroups of the automorphism group of its lattice vertex operator (super)algebra. In other words, the subgroups 224.M 24 and 223.M 23 of the automorphism group of the odd Leech lattice vertex operator algebra are non-split extensions. Our method can also confirm a similar result for the Conway group Co0 and the Leech lattice, which was already shown by Griess in [1]. This study is motivated by the moonshine-type observation on the N $$ \mathcal{N} $$ = 2 extremal elliptic genus of central charge 24 by Benjamin, Dyer, Fitzpatrick, and Kachru [2]. We also investigate weight-1 and weight- 3 2 $$ \frac{3}{2} $$ currents invariant under the subgroup 224.M 24 or 223.M 23 of the automorphism group of the odd Leech lattice vertex operator algebra, and revisit an N $$ \mathcal{N} $$ = 2 superconformal algebra in it. |
| format | Article |
| id | doaj-art-8f75b5186f5b4820bccc5e90267e87bb |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-8f75b5186f5b4820bccc5e90267e87bb2025-08-20T03:42:39ZengSpringerOpenJournal of High Energy Physics1029-84792025-06-012025615510.1007/JHEP06(2025)208On the symmetry of odd Leech lattice CFTMasaki Okada0Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of TokyoAbstract We show that the Mathieu groups M 24 and M 23 in the isometry group of the odd Leech lattice do not lift to subgroups of the automorphism group of its lattice vertex operator (super)algebra. In other words, the subgroups 224.M 24 and 223.M 23 of the automorphism group of the odd Leech lattice vertex operator algebra are non-split extensions. Our method can also confirm a similar result for the Conway group Co0 and the Leech lattice, which was already shown by Griess in [1]. This study is motivated by the moonshine-type observation on the N $$ \mathcal{N} $$ = 2 extremal elliptic genus of central charge 24 by Benjamin, Dyer, Fitzpatrick, and Kachru [2]. We also investigate weight-1 and weight- 3 2 $$ \frac{3}{2} $$ currents invariant under the subgroup 224.M 24 or 223.M 23 of the automorphism group of the odd Leech lattice vertex operator algebra, and revisit an N $$ \mathcal{N} $$ = 2 superconformal algebra in it.https://doi.org/10.1007/JHEP06(2025)208Conformal Field Models in String TheoryConformal and W SymmetryDiscrete Symmetries |
| spellingShingle | Masaki Okada On the symmetry of odd Leech lattice CFT Journal of High Energy Physics Conformal Field Models in String Theory Conformal and W Symmetry Discrete Symmetries |
| title | On the symmetry of odd Leech lattice CFT |
| title_full | On the symmetry of odd Leech lattice CFT |
| title_fullStr | On the symmetry of odd Leech lattice CFT |
| title_full_unstemmed | On the symmetry of odd Leech lattice CFT |
| title_short | On the symmetry of odd Leech lattice CFT |
| title_sort | on the symmetry of odd leech lattice cft |
| topic | Conformal Field Models in String Theory Conformal and W Symmetry Discrete Symmetries |
| url | https://doi.org/10.1007/JHEP06(2025)208 |
| work_keys_str_mv | AT masakiokada onthesymmetryofoddleechlatticecft |