An octonionic formulation of the M-theory algebra
High Energy Physics - Theory
2015-06-18 v1 Mathematical Physics
math.MP
Abstract
We give an octonionic formulation of the N = 1 supersymmetry algebra in D = 11, including all brane charges. We write this in terms of a novel outer product, which takes a pair of elements of the division algebra A and returns a real linear operator on A. More generally, with this product comes the power to rewrite any linear operation on R^n (n = 1,2,4,8) in terms of multiplication in the n-dimensional division algebra A. Finally, we consider the reinterpretation of the D = 11 supersymmetry algebra as an octonionic algebra in D = 4 and the truncation to division subalgebras.
Cite
@article{arxiv.1402.4649,
title = {An octonionic formulation of the M-theory algebra},
author = {A. Anastasiou and L. Borsten and M. J. Duff and L. J. Hughes and S. Nagy},
journal= {arXiv preprint arXiv:1402.4649},
year = {2015}
}