U-Duality and the Leech Lattice
Abstract
It has recently been shown that the full automorphism group of the Leech lattice, Conway's group Co_0, can be generated by 3 x 3 matrices over the octonions. We show such matrices are of type F_4 in E_{6(-26)}, the U-duality group for N=2, D=5 exceptional magic supergravity. By mapping points of the Leech lattice to black hole charge vectors, it is seen Co_0 is generated by U-duality transformations acting as rotations in the charge space for BPS black holes.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2013
- DOI:
- 10.48550/arXiv.1307.1554
- arXiv:
- arXiv:1307.1554
- Bibcode:
- 2013arXiv1307.1554R
- Keywords:
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- High Energy Physics - Theory;
- Mathematical Physics
- E-Print:
- 13 pages, construction clarified