More On The Connection Between Planar Field Theory And String Theory

TL;DR

This paper advances the understanding of how planar phi^3 theory on the world sheet relates to string formation by removing cutoffs and deriving a continuum limit, resulting in a string-like action from solitonic solutions.

Contribution

It introduces a continuum limit approach that yields a finite-energy string action from world sheet phi^3 theory, building on previous solitonic and zero mode analyses.

Findings

Successful removal of cutoff and transition to continuum limit

Derivation of a string-like action from world sheet theory

Identification of light modes with finite energies in the continuum

Abstract

We continue work on the connection between world sheet representation of the planar phi^3 theory and string formation. The present article, like the earlier work, is based on the existence of a solitonic solution on the world sheet, and on the zero mode fluctuations around this solution. The main advance made in this paper is the removal of the cutoff and the transition to the continuum limit on the world sheet. The result is an action for the modes whose energies remain finite in this limit (light modes). The expansion of this action about a dense background of graphs on the world sheet leads to the formation of a string.