On exact supersymmetry in DLCQ

In recent years a supersymmetric form of discrete light-cone quantization (hereafter `SDLCQʹ) has emerged as a very powerful tool for solving supersymmetric field theories. In this scheme, one calculates the light-cone supercharge with respect to a discretized light-cone Fock basis, instead of working with the light-cone Hamiltonian. This procedure has the advantage of preserving supersymmetry even in the discretized theory, and eliminates the need 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 Majorana fermion, which is known to be supersymmetric at a particular value of the fermion mass. After studying how singular-valued amplitudes and intermediate zero momentum modes are regularized in both schemes, we are able to establish a precise connection between conventional DLCQ and its supersymmetric extension, SDLCQ. In particular, we derive the explicit form of the (irrelevant) interaction that renders the DLCQ formulation of the theory exactly supersymmetric for any light-cone compactification. We check our analytical results via a numerical procedure, and discuss the relevance of this interaction when supersymmetry is explicitly broken.