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In this paper we construct super Yang-Mills theory in 10+2 dimensions, anumber of dimensions that was not reached before in a unitary supersymmetricfield theory, and show that this is the 2T-physics source of some cherishedlower dimensional field theories. The much studied conformally exact N=4 SuperYang-Mills field theory in 3+1 dimensions is known to be a compactified versionof N=1 SYM in 9+1 dimensions, while M(atrix) theory is obtained bycompactifications of the 9+1 theory to 0 dimensions (also 0+1 and others). Weshow that there is a deeper origin of these theories in two higher dimensionsas they emerge from the new theory with two times. Pursuing variousalternatives of gauge choices, solving kinematic equations and/or dimensionalreductions of the 10+2 theory, we suggest a web of connections that includethose mentioned above and a host of new theories that relate 2T-physics and1T-physics field theories, all of which have the 10+2 theory as the parent. Inaddition to establishing the higher spacetime underpinnings of these theories,a side benefit could be that in principle our approach can be used to developnew computational techniques.

Super Yang-Mills theory in 10+2 dimensions, The 2T-physics Source for N=4 SYM and M(atrix) Theory