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

Mean Field Method Applied To The New World Sheet Field Theory: String Formation

The present article is based on a previous one, where a second quantized field theory on the world sheet for summing the planar graphs of phi^3 theory was developed. In this earlier work, the ground state of the model was determined using a variational approximation. Here, starting with the same world sheet theory, we instead use the mean field method to compute the ground state, and find results in agreement with the variational calculation. Apart from serving as a check on the variational calculation, the mean field method enables us to go beyond the ground state to compute the excited states of the model. The spectrum of these states is that of a string with linear trajectories, plus a continuum that starts at higher energy. We show that, by appropriately tuning the parameters of the model, the string spectrum can be cleanly seperated from the continuum.Comment: 27 pages, 5 figures, typos 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

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

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

Planar Graphs On The World Sheet: The Hamiltonian Approach

The present work continues the program of summing planar Feynman graphs on the world sheet. Although it is based on the same classical action introduced in the earlier work, there are important new features: Instead of the path integral used in the earlier work, the model is quantized using the canonical algebra and the Hamiltonian picture. The new approach has an important advantage over the old one: The ultraviolet divergence that plagued the earlier work is absent. Using a family of projection operators, we are able to give an exact representation on the world sheet of the planar graphs of both the phi^3 theory, on which most of the previous work was based, and also of the phi^4 theory. We then apply the mean field approximation to determine the structure of the ground state. In agreement with the earlier work, we find that the graphs of phi^3 theory form a dense network (condensate) on the world sheet. In the case of the phi^4 theory, graphs condense for the unphysical (attractive) sign of the coupling, whereas there is no condensation for the physical (repulsive) sign.Comment: 32 pages, 6 figures, typos corrected and some minor clarifications adde