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The large N limit of exceptional Jordan matrix models and M, F theory

Abstract:

The large N → ∞ limits of the exceptional F<inf>4</inf>, E<inf>6</inf> Jordan matrix models of Smolin and Ohwashi lead to novel Chern-Simons membrane Lagrangians which are suitable candidates for providing a nonperturbative bosonic formulation of M theory in D = 27 real and complex dimensions, respectively. Freudenthal algebras and triple Freudenthal products permit the construction of a novelE<inf>7</inf> × S U (N) invariant matrix model whose large N limit yields generalized nonlinear sigma model actions on 28-complex-dimensional backgrounds associated with a 56-real-dimensional phase space realization of the Freudenthal algebra. We argue as to why the latter matrix model, in the large N limit, might be the proper arena for a bosonic formulation of F theory. Finally, we display generalized Dirac-Nambu-Goto membrane actions in terms of 3×3×3 cubic matrix entries that match the numbers of degrees of freedom of the 27-dimensional exceptional Jordan algebra J<inf>3</inf> [0]. © 2007 Elsevier Ltd. All rights reserved.