Introduction to transverse lattice gauge theory

I review a new treatment of an old idea for light-front quantization of lattice gauge theories and give new results from some illustrative calculations: [I] transverse lattice gauge theory; [II] pure glue; [III] heavy sources and winding modes; [IV] an example -- large-N QCD in 2+1 dimensions.Comment: 4 invited lectures, 21 pages, 7 figures, uses aipproc.st

The Weingarten Model a la Polyakov

The Weingarten lattice gauge model of Nambu-Goto strings is generalised to allow for fluctuations of an intrinsic worldsheet metric through a dynamical quadrilation. The continuum limit is taken for $c\leq1$ matter, reproducing the results of hermitian matrix models to all orders in the genus expansion. For the compact $c=1$ case the vortices are Wilson lines, whose exclusion leads to the theory of non-interacting fermions. As a by-product of the analysis one finds the critical behaviour of SOS and vertex models coupled to 2D quantum gravity.Comment: 16 pages (5 illustrations not included

Generalised Parton Distributions of the Pion on the Transverse Lattice

The quark generalised parton distributions of the pion are calculated from lightcone wavefunctions in transverse lattice gauge theory at large N_c. The pion effective size is found to decrease with increasing momentum transfer. An analytic ansatz, consistent with finite boundstate lightcone energy conditions, is given for the lightcone momentum dependence of the wavefunctions. This leads to simple, universal predictions for the behaviour of the distributions near the endpoints, complementing numerical DLCQ data.Comment: 9 pages, invited talk at Light-Cone 2004, Amsterdam, 16-20 August, 2004, to appear in proceedings; v2 resolves T-violation issu

Adjoint QCD2 and the Non-Abelian Schwinger Mechanism

Massless Majorana fermions in the adjoint representation of SU(N_c) are expected to screen gauge interactions in 1+1 dimensions, analogous to a similar Higgs phenomena known for 1+1-dimensional U(1) gauge theory with massless fundamental fermions (Schwinger model). Using the light-cone formalism and large-N_c limit, a non-abelian analogue of the Schwinger boson is shown to be responsible for the screening between heavy test charges. This adjoint boson does not exist simply as a physical state, but boundstates are built entirely from this particle.Comment: 10 pages LaTeX, uses boxedeps.tex. Figures clarified no

Collinear QCD Models

The small momentum fraction x behaviour of quarks in mesons is analysed in the 1+1-dimensional reduced model of large-N QCD by light-cone quantisation.Comment: 6 pages, LaTeX, uses boxedeps.tex (included). Invited talk at `New Non-Perturbative Methods and Quantisation on the Light-Cone', Les Houches 24 Feb - 4 Mar 1997. (To appear in proceedings). Replaced version has a (sign) typo corrected in very last sentenc

A Study of Heavy-Light Mesons on the Transverse Lattice

We present results from a study of meson spectra and structure in the limit where one quark is infinitely heavy. The calculations, based on the framework of light-front QCD formulated on a transverse lattice, are the first non-perturbative studies of B-mesons in light-front QCD. We calculate the Isgur-Wise form factor, light-cone distribution amplitude, the heavy-quark parton distribution function and the leptonic decay constant of B-mesons.Comment: 5 pages, 3 figures, Revtex, corrected typos, added references, included moment

c>1 Non-Critical Strings and Large-N Matrix Field Theory

Motivated by a possible relativistic string description of hadrons we use a discretised light-cone quantisation and Lanczos algorithm to investigate the phase structure of phi^3 matrix field theory in the large N limit. In 1+1 dimensions we confirm the existence of Polyakov's non-critical string theory at the boundary between parton-like and string-like phases, finding critical exponents for longitudinal oscillations equal to or consistent with those given by a mean field argument. The excitation spectrum is finite, possibly discrete. We calculate light-cone structure functions and find evidence that the probability Q(x) of a parton in the string carrying longitudinal momentum fraction between x and x+dx has support on all 0<x<1, despite the average number of partons being infinite.Comment: 9 pages LateX + 7 figures uuencode

Transverse Lattice

The transverse lattice approach to non-perturbative light-front hamiltonian QCD is described. Preliminary results on the pi-rho system are presented, at fixed DLCQ and Tamm-Dancoff cut-offs. A renormalised, approximately Lorentz covariant light-front hamiltonian is found to leading order of the colour-dielectric expansion, compatible with a massless pion. The pi light-front wavefunction is compared with experiment. Exclusive processes agree reasonably well, given the approximations, but inclusive processes, sensitive to higher Fock state structure, still exhibit large cut-off artifacts.Comment: 11 pages, Invited talk at Xth International Light-Cone Meeting on Non-Perturbative QCD and Hadron Phenomenology, Heidelberg 12-17 June 200

A (1+1)-Dimensional Reduced Model of Mesons

We propose an extension of 't Hooft's large-$N_c$ light-front QCD in two dimensions to include helicity and physical gluon degrees of freedom, modelled on a classical dimensional reduction of four dimensional QCD. A non-perturbative renormalisation of the infinite set of coupled integral equations describing boundstates is performed. These equations are then solved, both analytically in a phase space wavefunction approximation and numerically by discretising momenta, for (hybrid) meson masses and (polarized) parton structure functions.Comment: LaTex 13 pages; 2 figures, uuencoded file (PostScript