Supersymmetric Yang-Mills theories in D ⩾ 12 Original Research Article

We present supersymmetric Yang-Mills theories in arbitrary even dimensions with the signature (9+m, 1 +m) where m = 0, 1, 2,… beyond ten dimensions up to infinity. This formulation utilizes null-vectors and is a generalization of our previous work in 10+2 dimensions to arbitrary even dimensions with the above signature. We have overcome the previously observed obstruction beyond 11+3 dimensions, by the aid of projection operators. Both component and superspace formulations are presented. This also suggests the possibility of consistent supergravity theories in any even dimensions beyond 10+1 dimensions.