Supersymmetric Yang-Mills Theories in $D\ge 12$

Abstract

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.