String Field Theory of $c\leq 1$ Noncritical Strings

TL;DR

This paper develops a string field Hamiltonian for noncritical string theories with matter models like the Ising model, using only three string vertices, and discusses the necessary consistency conditions.

Contribution

It introduces a novel string field Hamiltonian for $c\,\leq\,1$ noncritical strings based on continuum limits of the Ising model, with a simplified vertex structure.

Findings

Constructed a string field Hamiltonian with three vertices.

Established a general consistency condition for such Hamiltonians.

Applied the framework to models with $c=1/2$ matter theory.

Abstract

We construct a string field Hamiltonian for a noncritical string theory with the continuum limit of the Ising model or its generalization as the matter theory on the worldsheet. It consists of only three string vertices as in the case for $c=0$. We also discuss a general consistency condition that should be satisfied by this kind of string field Hamiltonian.