The Geometry of Jordan Matrix Models

Details The Geometry of Jordan Matrix Models The Geometry of Jordan Matrix Models

2005-03-08

arxiv.org/abs/math-ph/0503015v3

Physics

Mathematical Physics

LaTeX, 11 pages, misprints corrected

Scientific paper

We elucidate the geometry of matrix models based on simple formally real Jordan algebras. Such Jordan algebras give rise to a nonassociative geometry that is a generalization of Lorentzian geometry. We emphasize constructions for the exceptional Jordan algebra and the exceptional Jordan C*-algebra and describe the projective spaces related to the exceptional cubic matrix model and the E_6 matrix model. The resulting projective spaces are shown to be exceptional versions of projective twistor space, thus revealing the existence of exceptional twistor string theories that are dual to octonionic matrix models.

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