Quantum Gravity and String Theory


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

Authors: Carlos Castro

The large N → ∞ limit of the Exceptional F4,E6 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 E7 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 J3[0].

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

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[v1] 24 Aug 2009

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