Field Theory On The World Sheet: Crystal Formation

TL;DR

This paper improves a world sheet field theory for planar phi^3 graphs by eliminating divergences and introducing a crystal background, resulting in a hybrid string-field model that fully manifests in the dense graph limit.

Contribution

It provides an improved treatment of divergences and introduces a crystal background, leading to a hybrid string-field model with a full string picture in the dense graph limit.

Findings

Ultraviolet divergence eliminated by renormalization.

Infrared divergence addressed by crystal background.

Full string picture emerges in the dense graph limit.

Abstract

In a previous work, a world sheet field theory which sums planar phi^3 graphs was investigated. In particular, a solitonic solution of this model was constructed, and quantum fluctuations around this solution led to a string picture. However, there were two problems which were not treated satisfactorily: An ultraviolet divergence and a spurious infrared divergence. Here we present an improved treatment, which eliminates the ultraviolet divergence in the normal fashion by mass and coupling constant renormalization. The infrared problem is taken care of by choosing a classical background which forms a one dimensional crystal. The resulting picture is a hybrid model with both string and underlying field theory excitations. Only in the dense graph limit on the world sheet a full string picture emerges.