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

Transverse Lattice QCD in 2+1 Dimensions

Following a suggestion due to Bardeen and Pearson, we formulate an effective light-front Hamiltonian for large-N gauge theory in (2+1)-dimensions. Two space-time dimensions are continuous and the remaining space dimension is discretised on a lattice. Eguchi-Kawai reduction to a (1+1)-dimensional theory takes place. We investigate the string tension and glueball spectrum, comparing with Euclidean Lattice Monte Carlo data.Comment: 4 pages LaTeX with 2 Postscript figures, uses boxedeps.tex and e spcrc2.sty. Poster session contribution to LATTICE96(poster). Minor changes in new versio

Glueball masses in the large N limit

The lowest-lying glueball masses are computed in SU($N$) gauge theory on a spacetime lattice for constant value of the lattice spacing $a$ and for $N$ ranging from 3 to 8. The lattice spacing is fixed using the deconfinement temperature at temporal extension of the lattice $N_T = 6$. The calculation is conducted employing in each channel a variational ansatz performed on a large basis of operators that includes also torelon and (for the lightest states) scattering trial functions. This basis is constructed using an automatic algorithm that allows us to build operators of any size and shape in any irreducible representation of the cubic group. A good signal is extracted for the ground state and the first excitation in several symmetry channels. It is shown that all the observed states are well described by their large $N$ values, with modest ${\cal O}(1/N^2)$ corrections. In addition spurious states are identified that couple to torelon and scattering operators. As a byproduct of our calculation, the critical couplings for the deconfinement phase transition for N=5 and N=7 and temporal extension of the lattice $N_T=6$ are determined.Comment: 1+36 pages, 22 tables, 21 figures. Typos corrected, conclusions unchanged, matches the published versio

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

Mesons on a transverse lattice

The meson eigenstates of the light-cone Hamiltonian in a coarse transverse lattice gauge theory are investigated. Building upon previous work in pure gauge theory, the Hamiltonian and its Fock space are expanded in powers of dynamical fields. In the leading approximation, the couplings appearing in the Hamiltonian are renormalised by demanding restoration of space-time symmetries broken by the cut-off. Additional requirements from chiral symmetry are discussed and difficulties in imposing them from first principles in the leading approximation are noted. A phenomenological calculation is then performed, in which chiral symmetry in spontaneously broken form is modelled by imposing the physical pion-rho mass splitting as a constraint. The light-cone wavefunctions of the resulting Hamiltonian are used to compute decay constants, form factors and quark momentum and spin distributions for the pion and rho mesons. Extensions beyond leading order, and the implications for first principles calculations, are briefly discussed.Comment: 31 pages, 7 figure

A Mean Field Approximation to the Worldsheet Model of Planar phi^3 Field Theory

We develop an approximation scheme for our worldsheet model of the sum of planar diagrams based on mean field theory. At finite coupling the mean field equations show a weak coupling solution that resembles the perturbative diagrams and a strong coupling solution that seems to represent a tensionless soup of field quanta. With a certain amount of fine-tuning, we find a solution of the mean field equations that seems to support string formation.Comment: 27 pages, 10 figures, typos corrected, appendix on slowly varying mean fields adde

Glueball calculations in large-N_c gauge theory

We use the light-front Hamiltonian of transverse lattice gauge theory to compute from first principles the glueball spectrum and light-front wavefunctions in the leading order of the 1/N_c colour expansion. We find 0^{++}, 2^{++}, and 1^{+-} glueballs having masses consistent with N_c=3 data available from Euclidean lattice path integral methods. The wavefunctions exhibit a light-front constituent gluon structure.Comment: 4 pages, 2 figures, uses macro boxedeps.tex, minor corrections in revised versio

W-Algebra Symmetries of Generalised Drinfel'd-Sokolov Hierarchies

Using the zero-curvature formulation, it is shown that W-algebra transformations are symmetries of corresponding generalised Drinfel'd-Sokolov hierarchies. This result is illustrated with the examples of the KdV and Boussinesque hierarchies, and the hierarchy associated to the Polyakov-Bershadsky W-algebra.Comment: 13 page