On Hexagonal Structures in Higher Dimensional Theories
High Energy Physics - Theory
2015-06-11 v1 Mathematical Physics
math.MP
Abstract
We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the compactification process from higher dimensions, or as dynamical string gauge groups; this includes groups like SU(2),SU(3), G_2, Spin(7), SO(8) as well as E_8 and SO(32). We emphasize also the relation of these hexagonal structures with the octonion division algebra, as we expect as well eventually some role for octonions in the interpretation of symmetries in High Energy Physics.
Cite
@article{arxiv.1209.0161,
title = {On Hexagonal Structures in Higher Dimensional Theories},
author = {Adil Belhaj and Luis J. Boya and Antonio Segui},
journal= {arXiv preprint arXiv:1209.0161},
year = {2015}
}
Comments
9 pages, Latex, 3 figures. Accepted for publication in International Journal of Theoretical Physics