  In this paper we construct super Yang-Mills theory in 10+2 dimensions, a
number of dimensions that was not reached before in a unitary supersymmetric
field theory, and show that this is the 2T-physics source of some cherished
lower dimensional field theories. The much studied conformally exact N=4 Super
Yang-Mills field theory in 3+1 dimensions is known to be a compactified version
of N=1 SYM in 9+1 dimensions, while M(atrix) theory is obtained by
compactifications of the 9+1 theory to 0 dimensions (also 0+1 and others). We
show that there is a deeper origin of these theories in two higher dimensions
as they emerge from the new theory with two times. Pursuing various
alternatives of gauge choices, solving kinematic equations and/or dimensional
reductions of the 10+2 theory, we suggest a web of connections that include
those mentioned above and a host of new theories that relate 2T-physics and
1T-physics field theories, all of which have the 10+2 theory as the parent. In
addition to establishing the higher spacetime underpinnings of these theories,
a side benefit could be that in principle our approach can be used to develop
new computational techniques.
