Renormalizing DLCQ using supersymmetry

Recent string theory developments suggest the necessity to understand supersymmetric gauge theories non-perturbatively, in various dimensions. In this work we show that there is a standard Hamiltonian formulation that generates a finite and supersymmetric result at every order of the approximation scheme known as discrete light-cone quantization (DLCQ). We present this renormalized DLCQ Hamiltonian and find that it has two novel features: it automatically chooses the ʹt Hooft prescription for renormalizing the singularities, and it introduces irrelevant operators that serve to preserve the supersymmetry and improve the convergence. We solve for the bound states and the wave functions with and without the irrelevant operators and verify that with the irrelevant operator the exact large-Nc supersymmetric DLCQ (SDLCQ) results are reproduced. With the irrelevant operator removed, we show that the bound-state mass and wave functions appear to be converging to the SDLCQ results but very slowly. This is a first step in extending the advantages of SDLCQ to non-supersymmetric theories.