## The Large N Limit of Exceptional Jordan Matrix Models and M, F Theory

**Authors:** Carlos Castro

The large N → ∞ limit of the Exceptional F_{4},E_{6} Jordan Matrix
Models of Smolin-Ohwashi leads to novel Chern-Simons Membrane Lagrangians
which are suitable candidates for a nonperturbative bosonic
formulation of M Theory in D = 27 real, complex dimensions, respectively.
Freudenthal algebras and triple Freudenthal products permits the
construction of a novel E_{7} X SU(N) invariant Matrix model whose large
N limit yields generalized nonlinear sigma models actions on 28 complex dimensional
backgrounds associated with a 56 real-dim phase space realization
of the Freudenthal algebra. We argue why the latter Matrix
Model, in the large N limit, might be the proper arena for a bosonic
formulation of F theory. To finalize we display generalized Dirac-Nambu-Goto
membrane actions in terms of 3 X 3 X 3 cubic matrix entries that
match the number of degrees of freedom of the 27-dim exceptional Jordan
algebra J_{3}[0].

**Comments:** 14 pages, This article appeared in the Journal of Geometry and Physics, 57 (2007) 1941-1949

**Download:** **PDF**

### Submission history

[v1] 24 Aug 2009

**Unique-IP document downloads:** 191 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*