Can DLCQ test the Maldacena Conjecture?

We consider the Maldacena conjecture applied to the near horizon geometry of a D1-brane in the supergravity approximation and consider the possibility of testing the conjecture against the boundary field theory calculation using DLCQ. We propose the two point function of the stress energy tensor as a convenient quantity that may be computed on both sides of the correspondence. On the supergravity side, we may invoke the methods of Gubser, Klebanov, Polyakov, and Witten. On the field theory side, we derive an explicit expression for the two point function in terms of data that may be extracted from a DLCQ calculation at a given harmonic resolution. This gives rise to a well defined numerical algorithm for computing the two point function, which we test in the context of free fermions and the 't Hooft model. For the supersymmetric Yang-Mills theory with 16 supercharges that arises in the Maldacena conjecture, the algorithm is perfectly well defined, although the size of the numerical computation grows too fast to admit any detailed analysis at present, and our results are only preliminary. We are, however, able to present more detailed results on the supersymmetric DLCQ computation of the stress energy tensor correlators for two dimensional Yang Mills theories with (1,1) and (2,2) supersymmetries.Comment: 19 pages, 5 figure

Matrix Theories from Reduced SU(N) Yang-Mills with Adjoint Fermions

We consider a dimensional reduction of 3+1 dimensional SU(N) Yang-Mills theory coupled to adjoint fermions to obtain a class of 1+1 dimensional matrix field theories. We derive the quantized light-cone Hamiltonian in the light-cone gauge A_- = 0 and large-N limit, and then solve for the masses, wavefunctions and structure functions of the color singlet ``meson-like'' and ``baryon-like'' boundstates. Among the states we study are many massless string-like states that can be solved for exactly.Comment: 13 pages, Revtex, one PS figur

N=1 super Yang-Mills on a (3+1) dimensional transverse lattice with one exact supersymmetry

We formulate ${\cal N}$=1 super Yang-Mills theory in 3+1 dimensions on a two dimensional transverse lattice using supersymmetric discrete light cone quantization in the large-$N_c$ limit. This formulation is free of fermion species doubling. We are able to preserve one supersymmetry. We find a rich, non-trivial behavior of the mass spectrum as a function of the coupling $g\sqrt{N_c}$, and see some sort of "transition" in the structure of a bound state as we go from the weak coupling to the strong coupling. Using a toy model we give an interpretation of the rich behavior of the mass spectrum. We present the mass spectrum as a function of the winding number for those states whose color flux winds all the way around in one of the transverse directions. We use two fits to the mass spectrum and the one that has a string theory justification appears preferable. For those states whose color flux is localized we present an extrapolated value for $m^2$ for some low energy bound states in the limit where the numerical resolution goes to infinity.Comment: 23(+2 for v3) pages, 19 figures; v2: a footnote added; v3: an appendix, comments, references added. The version to appear PR

Bound States of Dimensionally Reduced {SYM}_{2+1} at Finite N

We consider the dimensional reduction of N=1 {SYM}_{2+1} to 1+1 dimensions. The gauge groups we consider are U(N) and SU(N), where N is finite. We formulate the continuum bound state problem in the light-cone formalism, and show that any normalizable SU(N) bound state must be a superposition of an infinite number of Fock states. We also discuss how massless states arise in the DLCQ formulation for certain discretizations.Comment: 14 pages, REVTE

Effects of a fundamental mass term in two-dimensional super Yang-Mills theory

We show that adding a vacuum expectation value to a gauge field left over from a dimensional reduction of three-dimensional pure supersymmetric Yang-Mills theory generates mass terms for the fundamental fields in the two-dimensional theory while supersymmetry stays intact. This is similar to the adjoint mass term that is generated by a Chern-Simons term in this theory. We study the spectrum of the two-dimensional theory as a function of the vacuum expectation value and of the Chern-Simons coupling. Apart from some symmetry issues a straightforward picture arises. We show that at least one massless state exists if the Chern-Simons coupling vanishes. The numerical spectrum separates into (almost) massless and very heavy states as the Chern-Simons coupling grows. We present evidence that the gap survives the continuum limit. We display structure functions and other properties of some of the bound states.Comment: 17 pp., 10 figs; substantially revised version to be published in Phys. Rev.