## 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

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### Submission history

[v1] 24 Aug 2009

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