On exact supersymmetry in DLCQ

In recent years a supersymmetric form of discrete light-cone quantization t hereafter 'SDLCQ') has emerged as a very powerful tool for solving supersym metric field theories. In this scheme, one calculates the light-cone superc harge with respect to a discretized light-cone Fock basis, instead of worki ng with the light-cone Hamiltonian. This procedure has the advantage of pre serving supersymmetry even in the discretized theory, and eliminates the ne ed for explicit renormalizations in 1+1 dimensions. In order to compare the usual DLCQ prescription with the supersymmetric prescription, we consider two dimensional SU(N) Yang-Mills theory coupled to a massive adjoint Majora na fermion, which is known to be supersymmetric at a particular value of th e fermion mass. After studying how singular-valued amplitudes and intermedi ate zero momentum modes are regularized in both schemes, we are able to est ablish a precise connection between conventional DLCQ and its supersymmetri c extension, SDLCQ. In particular, we derive the explicit form of the (irre levant) interaction that renders the DLCQ formulation of the theory exactly supersymmetric for any Light-cone compactification. We check our analytica l results via a numerical procedure, and discuss the relevance of this inte raction when supersymmetry is explicitly broken. (C) 1998 Elsevier Science B.V. All rights reserved.