  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 AdS_n x S^m backgrounds. We show that all of these
supersymmetries are unified within the supersymmetry OSp(1/64), thus hinting
that the overall global spacetime symmetry of M-theory is OSp(1/64). We suggest
that the larger symmetries contained within OSp(1/64) 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 OSp(1/64)
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, AdS_n x S^m, etc., such that the linearly realized
part of OSp(1/64) is the global symmetry of the various dual sectors of
M-theory.
