[en] We consider the Maldacena conjecture applied to the near horizon geometry of a D1-brane in the supergravity approximation and present numerical results of a test of the conjecture against the boundary field theory calculation using supersymmetric discrete light-cone quantization (SDLCQ). We present numerical results with approximately 1000 times as many states as we previously considered. These results support the Maldacena conjecture and are within 10-15% of the predicted numerical results in some regions. Our results are still not sufficient to demonstrate convergence, and, therefore, cannot be considered to a numerical proof of the conjecture. We present a method for using a 'flavor' symmetry to greatly reduce the size of the basis and discuss a numerical method that we use which is particularly well suited for this type of matrix element calculation

[en] We report on progress in evaluating quantum filed theories with supersymmetric discrete light-cone quantization (SDLCQ). We compare the method to lattice gauge theory and point out its relevance for lattice calculations. As an exciting application we present a test of the Maldacena conjecture. We test the conjecture by evaluating the correlator of the stress-energy tensor in the strong coupling field theory and comparing to the string theory prediction of its behavior as a function of the distance. Our numerical results support the Maldacena conjecture and are within 10-15% of the predicted results

[en] Quantum field theories in front-form dynamics are not manifestly rotationally invariant. We study a model bound-state equation in 3+1 dimensional front-form dynamics, which was shown earlier to reproduce the Bohr and hyperfine structure of positronium. We test this model with regard to its rotational symmetry and find that rotational invariance is preserved to a high degree. Also, we find and quantify the expected dependence on the cut-off

[en] In this note we calculate the spectrum of two-dimensional QCD. We formulate the theory with SU(N_c) currents rather than with fermionic operators. We construct the Hamiltonian matrix in DLCQ formulation as a function of the harmonic resolution K and the numbers of flavors N_f and colors N_c . The resulting numerical eigenvalue spectrum is free from trivial multi-particle states which obscured previous results. The well-known 't Hooft and large N_f spectra are reproduced. In the case of adjoint fermions we present some new results

[en] Extending previous work, we calculate the fermionic spectrum of two-dimensional QCD (QCD₂) in the formulation with SU(N_c) currents. Together with the results in the bosonic sector this allows us to address the as yet unresolved task of finding the single-particle states of this theory as a function of the ratio of the numbers of flavors and colors, λ=N_f/N_c, anew. We construct the Hamiltonian matrix in the DLCQ formulation as an algebraic function of the harmonic resolution K and the continuous parameter λ in the Veneziano limit. We find that the fermion momentum is a function of λ in the discrete approach. A universality, existing only in two dimensions, dictates that the well-known 't Hooft and large N_f spectra be reproduced in the limits λ→0 and ∞, which we confirm. We identify their single-particle content which is surprisingly the same as in the bosonic sectors. All multiparticle states are classified in terms of their constituents. These findings allow for an identification of the lowest single particles of the adjoint theory. While we do not succeed in interpreting this spectrum completely, evidence is presented for the conjecture that adjoint QCD₂ has a bosonic and an independent fermionic Regge trajectory of single-particle states

[en] 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.

[en] We consider N=(1,1) super Yang-Mills theory in 1+1 dimensions with fundamentals at large N_c. A Chern-Simons term is included to give mass to the adjoint partons. Using the spectrum of the theory, we calculate thermodynamic properties of the system as a function of the temperature and the Yang-Mills coupling. In the large-N_c limit there are two noncommunicating sectors, the glueball sector, which we presented previously, and the mesonlike sector that we present here. We find that the mesonlike sector dominates the thermodynamics. Like the glueball sector, the meson sector has a Hagedorn temperature T_H, and we show that the Hagedorn temperature grows with the coupling. We calculate the temperature and coupling dependence of the free energy for temperatures below T_H. As expected, the free energy for weak coupling and low temperature grows quadratically with the temperature. Also the ratio of the free energies at strong coupling compared to weak coupling, r_s-w, for low temperatures grows quadratically with T. In addition, our data suggest that r_s-w tends to zero in the continuum limit at low temperatures

[en] In earlier work, N=(1,1) super Yang-Mills theory in two dimensions was found to have several interesting properties, though these properties could not be investigated in any detail. In this paper we analyze several of these properties. We investigate the spectrum of the theory, and we calculate the masses of the low-lying states using supersymmetric discrete light-cone quantization (SDLCQ) and obtain their continuum values. The spectrum exhibits an interesting pattern of masses, which we discuss along with a toy model for this pattern which might allow an understanding of the entire spectrum. We confirm an earlier speculation that the mass gap in this theory goes to zero at infinite resolution. We also discuss how the average number of partons in the bound states grows with increasing resolution. As a significant step toward a proof that SDLCQ must be supersymmetric, we determine the numbers of fermions and bosons in the N=(1,1) and N=(2,2) theories in each symmetry sector, as functions of the resolution, and show that these numbers are equal

[en] We solve N=(8,8) super-Yang-Mills theory in 1+1 dimensions at strong coupling to directly confirm the predictions of supergravity at weak coupling. We do our calculations in the large-N_c approximation using Supersymmetric Discrete Light-Cone Quantization with up to 3x10¹² basis states. We calculate the stress-energy correlator < T⁺⁺(r)T⁺⁺(0)> as a function of the separation r and find that at intermediate values of r the correlator behaves as r^-5 to within errors as predicted by weak-coupling supergravity. We also present an extension to significantly higher resolution of our earlier results for the same correlator in the N=(2,2) theory and see that in this theory the correlator has very different behavior at intermediate values of r

[en] We consider supersymmetric Yang-Mills theory on RxS¹xS¹. In particular, we choose one of the compact directions to be light like and another 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 the masses as functions of the longitudinal and transverse resolutions and show that the masses converge rapidly in both resolutions. We also study the behavior of the spectrum as a function of the coupling and find that at strong coupling there is a stable, well-defined spectrum which we present. We also find several unphysical states that decouple at large transverse resolution. There are two sets of massless states; one set is massless only at zero coupling and the other is massless at all couplings. Together these sets of massless states are in one-to-one correspondence with the full spectrum of the dimensionally reduced theory. (c) 2000 The American Physical Society