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Towards an Ashtekar formalism in eight dimensions

J. A. Nieto
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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.

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J. A. Nieto. 2005-02-17. Towards an Ashtekar formalism in eight dimensions. https://doi.org/10.1088/0264-9381%2F22%2F6%2F004

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