Gluon Chain Model of the Confining Force

We develop a picture of the QCD string as a chain of constituent gluons, bound by attractive nearest-neighbor forces which may be treated perturbatively. This picture accounts for both Casimir scaling at large N, and the asymptotic center dependence of the static quark potential. We discuss the relevance, to the gluon-chain picture, of recent three-loop results for the static quark potential. A variational framework is presented for computing the minimal energy and wavefunction of a long gluon chain, which enables us to derive both the logarithmic broadening of the QCD flux tube (``roughening''), and the existence of a Luscher -c/R term in the potential.Comment: 25 pages, 5 figures, latex2

The Size of a Polymer of String-Bits: A Numerical Investigation

In string-bit models, string is described as a polymer of point-like constituents. We attempt to use string-bit ideas to investigate how the size of string is affected by string interactions in a non-perturbative context. Lacking adequate methods to deal with the full complications of bit rearrangement interactions, we study instead a simplified analog model with only ``direct'' potential interactions among the bits. We use the variational principle in an approximate calculation of the mean-square size of a polymer as a function of the number of constituents/bits for various interaction strengths g in three specific models.Comment: 14 pages, LaTeX, 9 postscript figure

Renormalization of Quantum Fields on the Lightcone Worldsheet I: Scalar Fields

We show that the lightcone worldsheet formalism, constructed to represent the sum of the bare planar diagrams of scalar \phi^3 field theory, survives the renormalization procedure in space-time dimensions D not greater than 6. Specifically this means that all the counter-terms, necessary to produce a successful renormalized perturbation expansion to all orders, can be represented as local terms in the lightcone worldsheet action. Because the worldsheet regulator breaks Lorentz invariance, we find the need for two non-covariant counter-terms, in addition to the usual mass, coupling and wave function renormalization. One of these can be simply interpreted as a rescaling of transverse coordinates with respect to longitudinal coordinates. The second one introduces couplings between the matter and ghost worldsheet fields on the boundaries.Comment: 18 pages, 3 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