U-Duality and the Leech Lattice

TL;DR

This paper links the automorphism group of the Leech lattice to the U-duality group in supergravity, showing how black hole charge vectors relate to lattice symmetries and transformations.

Contribution

It demonstrates that the automorphism group of the Leech lattice can be realized within the U-duality group of a supergravity theory, connecting lattice symmetries to physical charge transformations.

Findings

Leech lattice automorphisms are represented by F_4 matrices in E_{6(-26)}.

Co_0 is generated by U-duality transformations acting on black hole charges.

Black hole charge vectors can be mapped to points in 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.