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

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

Bag Model for a Link in a Closed Gluonic Chain

The large $N_c$ limit of Yang-Mills gauge theory is the dynamics of a closed gluonic chain, but this fact does not obviate the inherently strong coupling nature of the dynamical problem. However, we suggest that a single link in such a chain might be reasonably described in the quasi-perturbative language of gluons and their interactions. To implement this idea, we use the MIT bag to model the physics of a nearest neighbor bond.Comment: 10 pages, LaTe

Universality and Clustering in 1+1 Dimensional Superstring-Bit Models

We construct a 1+1 dimensional superstring-bit model for D=3 Type IIB superstring. This low dimension model escapes the problems encountered in higher dimension models: (1) It possesses full Galilean supersymmetry; (2) For noninteracting polymers of bits, the exactly soluble linear superpotential describing bit interactions is in a large universality class of superpotentials which includes ones bounded at spatial infinity; (3) The latter are used to construct a superstring-bit model with the clustering properties needed to define an $S$-matrix for closed polymers of superstring-bits.Comment: 11 pages, Latex documen

Self Consistent Field Method for Planar phi^3 Theory

We continue and extend earlier work on the summation of planar graphs in phi^3 field theory, based on a local action on the world sheet. The present work employs a somewhat different version of the self consistent field (meanfield) approximation compared to the previous work on the same subject. Using this new approach, we are able to determine in general the asymptotic forms of the solutions, and in the case of one solution, even its exact form. This solution leads to formation of an unstable string, in agreement with the previous work. We also investigate and clarify questions related to Lorentz invariance and the renormalization of the solution.Comment: Latex, no other macros neede

Glueball spectrum in a (1+1)-dimensional model for QCD

We consider (1+1)-dimensional QCD coupled to scalars in the adjoint representation of the gauge group SU($N$). This model results from dimensional reduction of the (2+1)-dimensional pure glue theory. In the large-N limit we study the spectrum of glueballs numerically, using the discretized \lcq. We find a discrete spectrum of bound states, with the density of levels growing approximately exponentially with the mass. A few low-lying states are very close to being eigenstates of the parton number, and their masses can be accurately calculated by truncated diagonalizations.Comment: 17 pages, uses phyzzx and table.tex, 5 figures available upon request from [email protected]

Further Results about Field Theory on the World Sheet and String Formation

The present article is the continuation of the earlier work, which used the world sheet representation and the mean field approximation to sum planar graphs in massless phi^3 field theory. We improve on the previous work in two respects: A prefactor in the world sheet propagator that had been neglected is now taken into account. In addition, we introduce a non-zero bare mass for the field phi. Working with a theory with cutoff, and using the mean field approximation, we find that, depending on the range of values of the mass and coupling constant, the model has two phases: A string forming phase and a perturbative field theory phase. We also find the generation of a new degree of freedom, which was not in the model originally. The new degree of freedom can be thought of as the string slope, which is now promoted into a fluctuating dynamical variable. Finally, we show that the introduction of the bare mass makes it possible to renormalize the model.Comment: 39 pages, 10 figures, typos corrected and one equation simplifie

A Worldsheet Description of Large N_c Quantum Field Theory

The N_c to infinity limit of a matrix quantum field theory is equivalent to summing only planar Feynman diagrams. The possibility of interpreting this sum as some kind world-sheet theory has been in the air ever since 't Hooft's original paper. We establish here just such a world sheet description for a scalar quantum field with interaction term g\Tr\phi^3, and we indicate how the approach might be extended to more general field theories.Comment: 16 pages, 3 figures, latex, typos corrected, references added, interpretation of ghost determinant clarifie