Super Yang-Mills theory at weak, intermediate, and strong coupling - art. no. 085001

We consider three dimensional SU(N) N = 1 super-Yang-Mills theory compactif ied on the space-time R X S-1 X S-1. In particular, we compactify the light -cone coordinate x(-) on a light-like circle via DLCQ, and wrap the remaini ng transverse coordinate x(perpendicular to) on a spatial circle. By retain ing only the first few excited modes in the transverse direction, we are ab le to solve for bound state wave functions and masses numerically by diagon alizing the discretized light-cone supercharge. This regularization of the theory is shown to preserve supersymmetry. We plot bound state masses as a function of the coupling, showing the transition in particle masses as we m ove from a weakly to a strongly coupled theory. We analyze both numerically and analytically massless states which exist only in the limit of strong o r weak gauge coupling. In addition, we find massless states that persist fo r all values of the gauge coupling. An analytical treatment of these massle ss states is provided. Interestingly, in the strong coupling limit, these m assless states become string-like. [S0556-2821(99)03608-5].