# The exceptional Jordan algebra and the matrix string

@article{Smolin2001TheEJ, title={The exceptional Jordan algebra and the matrix string}, author={Lee Smolin}, journal={arXiv: High Energy Physics - Theory}, year={2001} }

A new matrix model is described, based on the exceptional Jordan algebra. The action is cubic, as in matrix Chern-Simons theory. We describe a compactification that, we argue, reproduces, at the one loop level, an octonionic compactification of the matrix string theory in which SO(8) is broken to G2. There are 27 matrix degrees of freedom, which under Spin(8) transform as the vector, spinor and conjugate spinor, plus three singlets, which represent the two longitudinal coordinates plus an…

## 57 Citations

### The Geometry of Jordan Matrix Models

- Mathematics
- 2005

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.…

### Matrix Model

- Computer Science
- 2002

It is of great interest that the properties of the product space Jc ×G, in which the degrees of freedom of the model live, are very similar to those of the physical Hilbert space.

### E6 Matrix Model

- Mathematics
- 2001

We consider a new matrix model based on the simply connected compact exceptional Lie group E6. A matrix Chern-Simons theory is directly derived from the invariant on E6 .I t is asserted that an…

### Matrix universality of gauge field and gravitational dynamics

- Physics
- 2008

A simple cubic matrix model is presented, which has truncations that, it is argued, lead at the classical level to a variety of theories of gauge fields and gravity. These include Chern-Simons theory…

### Exceptional Jordan matrix models, octonionic strings/branes and star product deformations

- Physics
- 2021

### On the Large N Limit of Exceptional Jordan Matrix Models, Chern-Simons Foliations and M, F Theory

- Mathematics
- 2007

The large N → ∞ limit of the Exceptional F4, E6 Jordan Matrix Models of Smolin-Ohwashi leads to a novel Chern-Simons Membrane Lagrangian which is the suitable candidate Lagrangian for…

### Trace dynamics and division algebras: towards quantum gravity and unification

- Physics
- 2020

Abstract We have recently proposed a Lagrangian in trace dynamics at the Planck scale, for unification of gravitation, Yang–Mills fields, and fermions. Dynamical variables are described by odd-grade…

### Exceptional Jordan Strings/Membranes and Octonionic Gravity/p-branes

- Mathematics
- 2011

Nonassociative Octonionic Ternary Gauge Field Theories are revisited paving the path to an analysis of the many physical applications of Exceptional Jordan Strings/Membranes and Octonionic Gravity.…

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