Meanfield Approximation For Field Theories On The Worldsheet Revisited

TL;DR

This paper revisits the mean field approximation for planar phi^3 theory on the world sheet, providing a systematic and analytically tractable approach that demonstrates string formation with proper coupling tuning.

Contribution

It introduces a simple, well-founded method for mean field approximation in world sheet field theories, improving upon previous approaches.

Findings

Analytical leading order mean field calculation achieved.

String formation observed with coupling constant tuning.

Provides a systematic framework for future studies.

Abstract

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.