The perils of 'soft' SUSY breaking

We consider a two dimensional SU(N) gauge theory coupled to an adjoint Majo rana fermion, which is known to be supersymmetric for a particular value of fermion mass. We investigate the 'soft' supersymmetry breaking of the disc rete light cone quantization (DLCQ) of this theory. There are several DLCQ formulations of this theory currently in the literature and they naively ap pear to behave differently under 'soft' supersymmetry breaking at finite re solution. We show that all these formulations nevertheless yield identical bound state masses in the decompactification limit of the light-like circle . Moreover, we are able to show that the supersymmetry-inspired version of DLCQ (so called 'SDLCQ') provides the best rate of convergence of DLCQ boun d state masses towards the actual continuum values, except possibly near or at the critical fermion mass. In this last case, we discuss improved extra polation schemes that must supplement the DLCQ algorithm in order to obtain correct continuum bound state masses. Interestingly, when we truncate the Fock space to two particles, the SDLCQ prescription presented here provides a scheme for improving the rate of convergence of the massive 't Hooft mod el. Thus the supersymmetry-inspired SDLCQ prescription is applicable to the ories without supersymmetry. (C) 1999 Published by Elsevier Science B.V. Al l rights reserved.