Towards an Ashtekar formalism in eight dimensions

Details Towards an Ashtekar formalism in eight dimensions Towards an Ashtekar formalism in eight dimensions

2004-10-27

arxiv.org/abs/hep-th/0410260v2

Class.Quant.Grav. 22 (2005) 947-955

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, Latex, minor changes, to appear in Class. Quantum Grav

Scientific paper

10.1088/0264-9381/22/6/004

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.

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