Lifting M-theory to two-time physics

M-theory has different global supersymmetry structures in its various dual incarnations, as characterized by the M-algebra in 11D, the type IIA, type-IIB, heterotic, type-I extended supersymmetries in 10D, and non-Abelian supersymmetries in the AdSn×Sm backgrounds. We show that all of these supersymmetries are unified within the supersymmetry OSp1/64, thus hinting that the overall global spacetime symmetry of M-theory is OSp1/64. We suggest that the larger symmetries contained within OSp1/64 which go beyond the familiar symmetries, are non-linearly realized hidden symmetries of M-theory. These can be made manifest by lifting 11D M-theory to the formalism of two-time physics in 13D by adding gauge degrees of freedom. We illustrate this idea by constructing a toy M-model on the worldline in 13D with manifest OSp1/64 global supersymmetry, and a number of new local symmetries that remove ghosts. Some of the local symmetries are bosonic cousins of kappa supersymmetries. The model contains 0-superbrane and p-forms (for p= 3, 6) as degrees of freedom. The gauge symmetries can be fixed in various ways to come down to a one time physics model in 11D, 10D, AdSn×Sm, etc., such that the linearly realized part of OSp1/64 is the global symmetry of the various dual sectors of M-theory.