Octonionic D=11 Supergravity and 'Octavian Integers' as Dilaton Vectors
High Energy Physics - Theory
2015-06-12 v2
Abstract
We formulate D=11 supergravity over the octonions by rewriting 32-component Majorana spinors as 4-component octonionic spinors. Dimensional reduction to D=4 and D=3 suggests an interpretation of the so-called 'dilaton vectors', which parameterise the couplings of the dilatons to other fields in the theory, as unit 'octavian integers' - the octonionic analogues of integers. The parameterisation involves a novel use of the duality between points and lines on the Fano plane, and suggests a series of consistent truncations with N=8,4,2,1, giving the 'four curious supergravities' studied by Duff and Ferrara
Cite
@article{arxiv.1502.02578,
title = {Octonionic D=11 Supergravity and 'Octavian Integers' as Dilaton Vectors},
author = {A. Anastasiou and M. J. Hughes},
journal= {arXiv preprint arXiv:1502.02578},
year = {2015}
}