Field Theory On The World Sheet: Improvements And Generalizations

TL;DR

This paper advances the world sheet field theory approach to planar phi^3 models, demonstrating solitonic ground states and string formation, with new results on energy bounds, stabilization, divergence treatment, and strong coupling expansion in various dimensions.

Contribution

It introduces several generalizations and improvements to the world sheet formulation, including energy bounds, stabilization methods, divergence handling, and systematic strong coupling expansion.

Findings

Solitonic ground states are confirmed in 1+2 and 1+3 dimensions.

Transverse string formation is observed around the soliton.

Ultraviolet divergences are better managed in higher dimensions.

Abstract

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.