Loop Gas Model for Open Strings

TL;DR

This paper models open strings in one-dimensional space using a loop gas approach on random surfaces, solving integral equations to analyze boundary conditions, operators, and string spectra.

Contribution

It introduces a loop gas (SOS) model for open strings, providing solutions for boundary conditions, operators, and spectra, and develops a Feynman diagram technique for string interactions.

Findings

Spectrum independent of string tension and quark mass

Constructed string propagator and analyzed excitations

Developed a diagrammatic approach for string interactions

Abstract

The open string with one-dimensional target space is formulated in terms of an SOS, or loop gas, model on a random surface. We solve an integral equation for the loop amplitude with Dirichlet and Neumann boundary conditions imposed on different pieces of its boundary. The result is used to calculate the mean values of order and disorder operators, to construct the string propagator and find its spectrum of excitations. The latter is not sensible neither to the string tension $\L$ nor to the mass $\mu$ of the ``quarks'' at the ends of the string. As in the case of closed strings, the SOS formulation allows to construct a Feynman diagram technique for the string interaction amplitudes.