The Perils of `Soft' SUSY Breaking

TL;DR

This paper investigates the effects of soft supersymmetry breaking in a two-dimensional SU(N) gauge theory with an adjoint Majorana fermion, comparing different DLCQ formulations and proposing improved extrapolation methods.

Contribution

It demonstrates the equivalence of various DLCQ formulations under soft SUSY breaking and shows SDLCQ's superior convergence, extending its applicability beyond supersymmetric theories.

Findings

All DLCQ formulations yield identical bound state masses in the decompactification limit.

SDLCQ provides the best convergence rate towards continuum bound state masses.

Improved extrapolation schemes are necessary near the critical fermion mass.

Abstract

We consider a two dimensional SU(N) gauge theory coupled to an adjoint Majorana fermion, which is known to be supersymmetric for a particular value of fermion mass. We investigate the `soft' supersymmetry breaking of the discrete light cone quantization (DLCQ) of this theory. There are several DLCQ formulations of this theory currently in the literature and they naively appear to behave differently under `soft' supersymmetry breaking at finite resolution. 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 bound state masses towards the actual continuum values, except possibly near or at the critical fermion mass. In this last case, we discuss improved extrapolation 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 model. Thus the supersymmetry-inspired SDLCQ prescription is applicable to theories without supersymmetry.