Towards an Ashtekar formalism in eight dimensions
J. A. Nieto
TL;DR
This paper explores extending the Ashtekar formalism to eight-dimensional spacetime using octonionic structures and a generalized MacDowell-Mansouri approach, potentially impacting M-theory formulations.
Contribution
It introduces a novel eight-dimensional Ashtekar formalism based on octonionic tensors and the MacDowell-Mansouri framework, expanding the mathematical tools for higher-dimensional theories.
Findings
Develops an octonionic tensor-based self-dual formalism in 8D
Links the formalism to M-theory via matroid theory
Provides a foundation for future higher-dimensional quantum gravity models
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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