3 N = ( 1 , 1 ) Super Yang – Mills on a ( 2 + 1 ) Dimensional Transverse Lattice with one Exact Supersymmetry

We present a formulation of N = (1, 1), Super Yang–Mills theory in 2+1 dimensions using a transverse lattice methods that exactly preserves one supersymmetry. First, using a Lagrangian approach we obtain a standard transverse lattice formulation of the Hamiltonian. We then show that the Hamiltonian also can be written discretely as the square of a supercharge and that this produces a different result. Problems associated with the discrete realization of the full supercharge algebra are discussed. Numerically we solve for the bound states of the theory in the large Nc approximation and we find good convergence. We show that the massive fermion and boson bound states are all exactly degenerate and that the number of fermion and boson massless bound states are closely related. Also we find that this theory admits winding states in the transverse direction and that their masses vary inversely with the winding number.