Covariant And Local Field Theory On The World Sheet

In earlier work, using the light cone picture, a world sheet field theory that sums planar phi^3 graphs was constructed and developed. Since this theory is both non-local and not explicitly Lorentz invariant, it is desirable to have a covariant and local alternative. In this paper, we construct such a covariant and local world sheet theory, and show that it is equivalent to the original non-covariant version.Comment: 22 pages,3 figures, typos and eqs.(11) and (63) are correcte

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

Meanfield Approximation For Field Theories On The Worldsheet Revisited

This work is the continuation of the earlier efforts to apply the mean field approximation to the world sheet formulation of planar phi^3 theory. The previous attempts were either simple but without solid foundation or well founded but excessively complicated. In this article, we present an approach both simple, and also systematic and well founded. We are able to carry through the leading order mean field calculation analytically, and with a suitable tuning of the coupling constant, we find string formation.Comment: 38 pages, 8 figures, late

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

The Conformal Points Of The Generalized Thirring Model

The conformal fixed points of the generalized Thirring model are investigated with the help of bosonization, the large N limit and the operator product expansion. Necessary conditions on the coupling constants for conformal invariance are derived.Comment: 19 pages (latex, no other macros needed); LBL-35842, UCB-PTH-94/1

Field Theory On The World Sheet: Improvements And Generalizations

This article is the continuation of a project of investigating planar phi^3 model in various dimensions. The idea is to reformulate them on the world sheet, and then to apply the classical (meanfield) approximation, with two goals: To show that the ground state of the model is a solitonic configuration on the world sheet, and the quantum fluctuations around the soliton lead to the formation of a transverse string. After a review of some of the earlier work, we introduce and discuss several generalizations and new results. In 1+2 dimensions, a rigorous upper bound on the solitonic energy is established. A phi^4 interaction is added to stabilize the original phi^3 model. In 1+3 and 1+5 dimensions, an improved treatment of the ultraviolet divergences is given. And significantly, we show that our approximation scheme can be imbedded into a systematic strong coupling expansion. Finally, the spectrum of quantum fluctuations around the soliton confirms earlier results: In 1+2 and 1+3 dimensions, a transverse string is formed on the world sheet.Comment: 29 pages, 5 figures, several typos and eqs.(74) and (75) are corrected, a comment added to section

More On The Connection Between Planar Field Theory And String Theory

We continue work on the connection between world sheet representation of the planar phi^3 theory and string formation. The present article, like the earlier work, is based on the existence of a solitonic solution on the world sheet, and on the zero mode fluctuations around this solution. The main advance made in this paper is the removal of the cutoff and the transition to the continuum limit on the world sheet. The result is an action for the modes whose energies remain finite in this limit (light modes). The expansion of this action about a dense background of graphs on the world sheet leads to the formation of a string.Comment: 27 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

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 Worldsheet Description of Planar Yang-Mills Theory

We extend previous work by developing a worldsheet description of non-abelian gauge theory (Yang-Mills). This task requires the introduction of Grassmann variables on the world sheet analogous to those of the Neveu-Schwarz-Ramond formulation of string theory. A highlight of our construction is that once the three gluon vertices of Yang-Mills Feynman diagrams are given a worldsheet description, the worldsheet formalism automatically produces all of the quartic vertices.Comment: 18 pages, 15 figures, reference added, paragraph added to section 3.3, erroneous statement in section 4 corrected, typos correcte