Scalar Field Theories On The World Sheet: Cutoff Independent Treatment

TL;DR

This paper develops a cutoff-independent scalar field theory on the world sheet by eliminating singularities through a mass counter term, leading to a string-like model with curved trajectories.

Contribution

It introduces a method to remove both infrared and ultraviolet divergences in world sheet scalar theories, enabling a continuous, cutoff-free formulation.

Findings

Successfully removes cutoff dependence in the model

Finds solitonic solutions in the mean field approximation

Derives a string-like model with curved trajectories

Abstract

Following earlier work on the same topic, we consider once more scalar field theories on the world sheet parametrized by the light cone coordinates. For most of the way, we use the same approach as in the previous work, but there is an important new development. To avoid the light cone singularity at p^{+}=0, one world sheet coordinate had to be discretized, introducing a cutoff into the model.In the earlier work, this cutoff could not be removed, making the model unreliable. In the present article, we show that, by a careful choice of the mass counter term, both the infrared singularity at p^{+}=0 and the ultraviolet mass divergences can be simultaneously eliminated. We therefore finally have a cutoff independent model on a continuously parametrized world sheet. We study this model in the mean field approximation, and as before, we find solitonic solutions. Quantizing the solitonic collective coordinates gives rise to a string like model. However, in contrast to the standard string model, the trajectories here are not in general linear but curved.