Towards an Ashtekar formalism in eight dimensions
High Energy Physics - Theory
2009-11-10 v2
Abstract
We investigate the possibility of extending the Ashtekar theory to eight dimensions. Our approach relies on two notions: the octonionic structure and the MacDowell-Mansouri formalism generalized to a spacetime of signature 1+7. The key mathematical tool for our construction is the self-dual (antiself-dual) four-rank fully antisymmetric octonionic tensor. Our results may be of particular interest in connection with a possible formulation of M-theory via matroid theory.
Keywords
Cite
@article{arxiv.hep-th/0410260,
title = {Towards an Ashtekar formalism in eight dimensions},
author = {J. A. Nieto},
journal= {arXiv preprint arXiv:hep-th/0410260},
year = {2009}
}
Comments
15 pages, Latex, minor changes, to appear in Class. Quantum Grav