Super Yang-Mills theory at weak, intermediate, and strong coupling

We consider three dimensional (Formula presented) super-Yang-Mills theory compactified on the space-time (Formula presented). In particular, we compactify the light-cone coordinate (Formula presented) on a light-like circle via DLCQ, and wrap the remaining transverse coordinate (Formula presented) on a spatial circle. By retaining only the first few excited modes in the transverse direction, we are able to solve for bound state wave functions and masses numerically by diagonalizing 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 move from a weakly to a strongly coupled theory. We analyze both numerically and analytically massless states which exist only in the limit of strong or weak gauge coupling. In addition, we find massless states that persist for all values of the gauge coupling. An analytical treatment of these massless states is provided. Interestingly, in the strong coupling limit, these massless states become string-like.