Numerical Simulations of N=(1,1) SYM{1+1} with Large Supersymmetry Breaking

We consider the $N=(1,1)$ SYM theory that is obtained by dimensionally reducing SYM theory in 2+1 dimensions to 1+1 dimensions and discuss soft supersymmetry breaking. We discuss the numerical simulation of this theory using SDLCQ when either the boson or the fermion has a large mass. We compare our result to the pure adjoint fermion theory and pure adjoint boson DLCQ calculations of Klebanov, Demeterfi, and Bhanot and of Kutasov. With a large boson mass we find that it is necessary to add additional operators to the theory to obtain sensible results. When a large fermion mass is added to the theory we find that it is not necessary to add operators to obtain a sensible theory. The theory of the adjoint boson is a theory that has stringy bound states similar to the full SYM theory. We also discuss another theory of adjoint bosons with a spectrum similar to that obtained by Klebanov, Demeterfi, and Bhanot.Comment: 12 pages, 4 figure

The Perils of `Soft' SUSY Breaking

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.Comment: 11 pages, Latex; 2 figures (EPS); Numerical results extended; conclusions revise

Wave functions and properties of massive states in three-dimensional supersymmetric Yang-Mills theory

We apply supersymmetric discrete light-cone quantization (SDLCQ) to the study of supersymmetric Yang-Mills theory on R x S^1 x S^1. One of the compact directions is chosen to be light-like and the other to be space-like. Since the SDLCQ regularization explicitly preserves supersymmetry, this theory is totally finite, and thus we can solve for bound-state wave functions and masses numerically without renormalizing. We present an overview of all the massive states of this theory, and we see that the spectrum divides into two distinct and disjoint sectors. In one sector the SDLCQ approximation is only valid up to intermediate coupling. There we find a well defined and well behaved set of states, and we present a detailed analysis of these states and their properties. In the other sector, which contains a completely different set of states, we present a much more limited analysis for strong coupling only. We find that, while these state have a well defined spectrum, their masses grow with the transverse momentum cutoff. We present an overview of these states and their properties.Comment: RevTeX, 25 pages, 16 figure

Simulation of Dimensionally Reduced SYM-Chern-Simons Theory

A supersymmetric formulation of a three-dimensional SYM-Chern-Simons theory using light-cone quantization is presented, and the supercharges are calculated in light-cone gauge. The theory is dimensionally reduced by requiring all fields to be independent of the transverse dimension. The result is a non-trivial two-dimensional supersymmetric theory with an adjoint scalar and an adjoint fermion. We perform a numerical simulation of this SYM-Chern-Simons theory in 1+1 dimensions using SDLCQ (Supersymmetric Discrete Light-Cone Quantization). We find that the character of the bound states of this theory is very different from previously considered two-dimensional supersymmetric gauge theories. The low-energy bound states of this theory are very ``QCD-like.'' The wave functions of some of the low mass states have a striking valence structure. We present the valence and sea parton structure functions of these states. In addition, we identify BPS-like states which are almost independent of the coupling. Their masses are proportional to their parton number in the large-coupling limit.Comment: 18pp. 7 figures, uses REVTe

On Exact Supersymmetry in DLCQ

In recent years a supersymmetric form of discrete light-cone quantization (hereafter `SDLCQ') 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.Comment: 12 page

On the Transition from Confinement to Screening in QCD_{1+1} Coupled to Adjoint Fermions at Finite N

We consider SU(N) QCD_{1+1} coupled to massless adjoint Majorana fermions, where N is finite but arbitrary. We examine the spectrum for various values of N, paying particular attention to the formation of multi-particle states, which were recently identified by Gross, Hashimoto and Klebanov in the N -> infinity limit of the theory. It is believed that in the limit of vanishing fermion mass, there is a transition from confinement to screening in which string-like states made out of adjoint fermion bits dissociate into stable constituent ``single particles''. In this work, we provide numerical evidence that such a transition into stable constituent particles occurs not only at large N, but for any finite value of N. In addition, we discuss certain issues concerning the ``topological'' properties exhibited by the DLCQ spectrum.Comment: 14 pages, Late

The String Tension in Two Dimensional Gauge Theories

We review and elaborate on properties of the string tension in two-dimensional gauge theories. The first model we consider is massive QED in the $m\ll e$ limit. We evaluate the leading string tension both in the fermionic and bosonized descriptions. We discuss the next to leading corrections in $m/e$. The next-to-leading terms in the long distance behavior of the quark-antiquark potential, are evaluated in a certain region of external versus dynamical charges. The finite temperature behavior is also determined. In $QCD_2$ we review the results for the string tension of quarks in cases with dynamical quarks in the fundamental, adjoint, symmetric and antisymmetric representations. The screening nature of $SYM_2$ is re-derived.Comment: 25 pages, Latex. v2: several changes, mainly in section

The Light-Cone Vacuum in 1+1 Dimensional Super-Yang-Mills Theory

The Discrete Light-Cone Quantization (DLCQ) of a supersymmetric SU(N) gauge theory in 1+1 dimensions is discussed, with particular emphasis given to the inclusion of all dynamical zero modes. Interestingly, the notorious `zero-mode problem' is now tractable because of special supersymmetric cancellations. In particular, we show that anomalous zero-mode contributions to the currents are absent, in contrast to what is observed in the non-supersymmetric case. We find that the supersymmetric partner of the gauge zero mode is the diagonal component of the fermion zero mode. An analysis of the vacuum structure is provided and it is shown that the inclusion of zero modes is crucial for probing the phase properties of the vacua. In particular, we find that the ground state energy is zero and N-fold degenerate, and thus consistent with unbroken supersymmetry. We also show that the inclusion of zero modes for the light-cone supercharges leaves the supersymmetry algebra unchanged. Finally, we remark that the dependence of the light-cone Fock vacuum in terms of the gauge zero is unchanged in the presence of matter fields.Comment: REVTEX, 15 page