An Improved Mean Field Approximation on the Worldsheet for Planar phi^3 Theory

TL;DR

This paper improves the mean field approximation method on the world sheet for planar phi^3 theory, deriving equations that suggest the formation of metastable string solutions without additional approximations.

Contribution

It introduces an enhanced mean field approach on the world sheet for phi^3 theory, deriving equations that reveal potential string formation.

Findings

Equations suggest metastable string forming solutions

No additional approximations used beyond previous work

Method applicable to summing planar graphs in phi^3 theory

Abstract

We present an improved version of our earlier work on summing the planar graphs in phi^3 field theory. The present treatment is also based on our world sheet formalism and the mean field approximation, but it makes use of no further approximations. We derive a set of equations between the expectation values of the world sheet fields, and we investigate them in certain limits. We show that the equations can give rise to (metastable) string forming solutions.