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

The large N→∞N→∞ limits of the exceptional F4,E6F4,E6 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 MM theory in D=27D=27 real and complex dimensions, respectively. Freudenthal algebras and triple Freudenthal products permit the construction of a novel  E7×SU(N)E7×SU(N) invariant matrix model whose large NN 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 NN limit, might be the proper arena for a bosonic formulation of FF 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 J3[0]J3[0].