A derivation of Regge trajectories in large-N transverse lattice QCD

Large-N QCD is analysed in light-front coordinates with a transverse lattice at strong coupling. The general formalism can be looked up on as a d+n expansion with a stack of d-dimensional hyperplanes uniformly spaced in n transverse dimensions. It can arise by application of the renormalisation group transformations only in the transverse directions. At leading order in strong coupling, the gauge field dynamics reduces to the constraint that only colour singlet states can jump between the hyperplanes. With d=2, n=2 and large-N, the leading order strong coupling results are simple renormalisations of those for the 't Hooft model. The meson spectrum lies on a set of parallel trajectories labeled by spin. This is the first derivation of the widely anticipated Regge trajectories in a regulated systematic expansion in QCD.Comment: Lattice 2000 (spectrum), 5 pages, to appear in the proceeding

String Spectrum of 1+1-Dimensional Large N QCD with Adjoint Matter

We propose gauging matrix models of string theory to eliminate unwanted non-singlet states. To this end we perform a discretised light-cone quantisation of large N gauge theory in 1+1 dimensions, with scalar or fermionic matter fields transforming in the adjoint representation of SU(N). The entire spectrum consists of bosonic and fermionic closed-string excitations, which are free as N tends to infinity. We analyze the general features of such bound states as a function of the cut-off and the gauge coupling, obtaining good convergence for the case of adjoint fermions. We discuss possible extensions of the model and the search for new non-critical string theories.Comment: 20 pages (7 figures available from authors as postscipt files), PUPT-134

Colour-Dielectric Gauge Theory on a Transverse Lattice

We investigate in some detail consequences of the effective colour-dielectric formulation of lattice gauge theory using the light-cone Hamiltonian formalism with a transverse lattice. As a quantitative test of this approach, we have performed extensive analytic and numerical calculations for 2+1-dimensional pure gauge theory in the large N limit. Because of Eguchi-Kawai reduction, one effectively studies a 1+1-dimensional gauge theory coupled to matter in the adjoint representation. We study the structure of coupling constant space for our effective potential by comparing with the physical results available from conventional Euclidean lattice Monte Carlo simulations of this system. In particular, we calculate and measure the scaling behaviour of the entire low-lying glueball spectrum, glueball wavefunctions, string tension, asymptotic density of states, and deconfining temperature. We employ a new hybrid DLCQ/wavefunction basis in our calculations of the light-cone Hamiltonian matrix elements, along with extrapolation in Tamm-Dancoff truncation, significantly reducing numerical errors. Finally we discuss, in light of our results, what further measurements and calculations could be made in order to systematically remove lattice spacing dependence from our effective potential a priori.Comment: 48 pages, Latex, uses macro boxedeps.tex, minor errors corrected in revised versio

Transverse Lattice Approach to Light-Front Hamiltonian QCD

We describe a non-perturbative procedure for solving from first principles the light-front Hamiltonian problem of SU(N) pure gauge theory in D spacetime dimensions (D>2), based on enforcing Lorentz covariance of observables. A transverse lattice regulator and colour-dielectric link fields are employed, together with an associated effective potential. We argue that the light-front vacuum is necessarily trivial for large enough lattice spacing, and clarify why this leads to an Eguchi-Kawai dimensional reduction of observables to 1+1-dimensions in the infinite N limit. The procedure is then tested by explicit calculations for 2+1-dimensional SU(infinity) gauge theory, within a first approximation to the lattice effective potential. We identify a scaling trajectory which produces Lorentz covariant behaviour for the lightest glueballs. The predicted masses, in units of the measured string tension, are in agreement with recent results from conventional Euclidean lattice simulations. In addition, we obtain the potential between heavy sources and the structure of the glueballs from their light-front wavefunctions. Finally, we briefly discuss the extension of these calculations to 3+1-dimensions.Comment: 55 pages, uses macro boxedeps.tex, minor corrections in revised versio

QCD strings and the thermodynamics of the metastable phase of QCD at large NcN_c

The thermodyanmics of a metastable hadronic phase of QCD at large $N_C$ are related to properties of an effective QCD string. In particular, it is shown that in the large $N_c$ limit and near the maximum hadronic temperature, $T_H$, the energy density and pressure of the metastable phase scale as ${\cal E} \sim (T_H-T)^{-(D_\perp-6)/2}$ (for $D_\perp <6$) and $P \sim (T_H-T)^{-(D_\perp-4)/2}$ (for $D_\perp <4$) where $D_\perp$ is the effective number of transverse dimensions of the string theory. It is shown, however, that for the thermodynamic quantities of interest the limits $T \to T_H$ and $N_c \to \infty$ do not commute. The prospect of extracting $D_\perp$ via lattice simulations of the metastable hadronic phase at moderately large $N_c$ is discussed.Comment: After this paper was published, the author became aware of an important early paper by Charles Thorn on the subject of the QCD phase transition at large N_c and its relation to the Hagedorn spectrum. Given the pioneering nature of Thorn's paper, and the fact that it is not as widely known as it should be, it is important to cite it in the present work. This updated version cites Thorn's wor

On the Spectrum of QCD(1+1) with SU(N_c) Currents

Extending previous work, we calculate in this note the fermionic spectrum of two-dimensional QCD (QCD_2) in the formulation with SU(N_c) currents. Together with the results in the bosonic sector this allows 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, \lambda=N_f/N_c, anew. We construct the Hamiltonian matrix in DLCQ formulation as an algebraic function of the harmonic resolution K and the continuous parameter \lambda. Amongst the more surprising findings in the fermionic sector chiefly considered here is that the fermion momentum is a function of \lambda. This dependence is necessary in order to reproduce the well-known 't Hooft and large N_f spectra. Remarkably, those spectra have the same single-particle content as the ones in the bosonic sectors. The twist here is the dramatically different sizes of the Fock bases in the two sectors, which makes it possible to interpret in principle all states of the discrete approach. The hope is that some of this insight carries over into the continuum. We also present some new findings concerning the single-particle spectrum of the adjoint theory.Comment: 21 pp., 13 figures, version published in PR

Universality in Two Dimensional Gauge Theory.

We discuss two dimensional Yang -- Mills theories with massless fermions in arbitrary representations of a gauge group $G$. It is shown that the physics (spectrum and interactions) of the massive states in such models is independent of the detailed structure of the model, and only depends on the gauge group $G$ and an integer $k$ measuring the total anomaly. The massless physics, which does depend on the details of the model, decouples (almost) completely from that of the massive one. As an example, we discuss the equivalence of QCD$_2$ coupled to fermions in the adjoint, and fundamental representations.Comment: 16 pages, harvma

Exact Solution of the One-Dimensional Non-Abelian Coulomb Gas at Large N

The problem of computing the thermodynamic properties of a one-dimensional gas of particles which transform in the adjoint representation of the gauge group and interact through non-Abelian electric fields is formulated and solved in the large $N$ limit. The explicit solution exhibits a first order confinement-deconfinement phase transition with computable properties and describes two dimensional adjoint QCD in the limit where matter field masses are large.Comment: 8 pages, late