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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Main Author: Masaki Okada
Format: Article
Language:English
Published: SpringerOpen 2025-06-01
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.
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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