U-Duality and the Leech Lattice
High Energy Physics - Theory
2018-04-05 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1307.1554,
title = {U-Duality and the Leech Lattice},
author = {Michael Rios},
journal= {arXiv preprint arXiv:1307.1554},
year = {2018}
}
Comments
13 pages, construction clarified