  Starting with the ordinary ten-dimensional supersymmetric Yang-Mills theory
for the gauge group U(N), we obtain a twelve-dimensional supersymmetric gauge
theory as the large N limit. The two symplectic canonical coordinates
parametrizing the unitary N X N matrices for U(N) are identified with the extra
coordinates in twelve dimensions in the $N\to\infty$ limit. Applying further a
strong/weak duality, we get the `decompactified' twelve-dimensional theory. The
resulting twelve-dimensional theory has peculiar gauge symmetry which is
compatible also with supersymmetry. We also establish a corresponding new
superspace formulation with the extra coordinates. By performing a dimensional
reduction from twelve dimensions directly into three dimensions, we see that
the Poisson bracket terms which are needed for identification with
supermembrane action arises naturally. This result indicates an universal
duality mechanism that the 't Hooft limit of an arbitrary supersymmetric theory
promotes the original supersymmetric theory in (D-1,1) dimensions into a theory
in (D,2) dimensions with an additional pair of space-time coordinates. This
also indicates interesting dualities between supermembrane theory, type IIA
superstring with D0-branes, and the recently-discovered twelve-dimensional
supersymmetric theories.
