Renormalizing DLCQ using supersymmetry

Recent string theory developments suggest the necessity to understand super symmetric gauge theories non-perturbatively, in various dimensions. In this work we show that there is a standard Hamiltonian formulation that generat es a finite and supersymmetric result at every order of the approximation s cheme known as discrete light-cone quantization (DLCQ), We present this ren ormalized DLCQ Hamiltonian and find that it has two novel features: it auto matically chooses the 't Hooft prescription for renormalizing the singulari ties, and it introduces irrelevant operators that serve to preserve the sup ersymmetry and improve the convergence. We solve for the bound states and t he wave functions with and without the irrelevant operators and verify that with the irrelevant operator the exact large-N-C supersymmetric DLCQ (SDLC Q) results are reproduced. With the irrelevant operator removed, we show th at the hound-state mass and wave functions appear to he converging to the S DLCQ results but very slowly. This is a first step in extending the advanta ges of SDLCQ to non-supersymmetric theories. (C) 2001 Published by Elsevier Science B.V.