The Geometry of Jordan Matrix Models
arXiv:math-ph/0503015
Abstract
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.
LaTeX, 11 pages, misprints corrected
References in corpus (11)
- M Theory As A Matrix Model: A Conjecture
- A Large-N Reduced Model as Superstring
- Tachyon Condensation on the Brane Antibrane System
- A Standard Model from the E8 x E8 Heterotic Superstring
- Lectures on Twistor Strings and Perturbative Yang-Mills Theory
- Exceptional Projective Geometries and Internal Symmetries
- The cubic matrix model and a duality between strings and loops
- The Exceptional Jordan Eigenvalue Problem
- Computability at the Planck scale
- On Tachyon Condensation of Intersecting Noncommutative Branes in M(atrix) Theory
- On a Jordan-algebraic formulation of quantum mechanics: Hilbert space construction