6-Vertex Model on an Open String Worldsheet

TL;DR

This paper demonstrates how a 6-vertex model with boundary conditions on an open string worldsheet can describe a compactified target space coordinate, illustrating Bethe ansatz application with boundaries.

Contribution

It extends the 6-vertex model framework to open string worldsheets with boundary conditions, linking vertex weights to target space compactification.

Findings

Target space coordinate is compactified on a circle of radius R.

Bethe ansatz is applicable in the presence of boundaries.

Continuum limit connects lattice model to string target space.

Abstract

We propose boundary conditions on a two dimensional 6-vertex model, which is defined on the lightcone lattice for an open string worldsheet. We show that, in the continuum limit, the degrees of freedom of this 6-vertex model describe a target space coordinate compactified on a circle of radius R, which is related to the vertex weights. This conclusion had already been established for the case of a 6-vertex model on the worldsheet lattice for the propagator of a closed string. This exercise illustrates how the Bethe ansatz works in the presence of boundaries, at least of this particular type.