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

TL;DR

This paper advances the understanding of string formation in phi^3 field theory by incorporating a corrected propagator, a non-zero bare mass, and analyzing phase transitions and new degrees of freedom using mean field approximation.

Contribution

It improves previous world sheet models by including a propagator prefactor and bare mass, revealing phase structure and a dynamical string slope as a new degree of freedom.

Findings

Identification of string forming and perturbative phases

Generation of a new dynamical degree of freedom (string slope)

Renormalization enabled by introducing bare mass

Abstract

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.