Matrix Models and One Dimensional Open String Theory (Revised)

TL;DR

This paper introduces a matrix model for one-dimensional open strings, revealing its equivalence to a fermionic system with long-range interactions, and explores its scaling limits and boundary conditions.

Contribution

It presents a novel matrix model for D=1 open strings, analyzing its equivalence to fermions with spin and long-range interactions, and investigates different boundary conditions and their effects.

Findings

Identified two scaling limits with distinct boundary conditions.

Calculated the free energy and boundary cosmological constant.

Discussed potential analogs of the Das-Jevicki field for open string tachyons.

Abstract

We propose a random matrix model as a representation for $D=1$ open strings. We show that the model is equivalent to $N$ fermions with spin in a central potential that also includes a long-range ferromagnetic interaction between the fermions that falls off as $1/(r_{ij})^2$. We find two interesting scaling limits and calculate the free energy for both situations. One limit corresponds to Dirichlet boundary conditions for the dual graphs and the other corresponds to Neumann conditions. We compute the boundary cosmological constant and show that it is of order $1/\log(\beta)$. We also briefly discuss a possible analog of the Das-Jevicki field for the open string tachyon. (n.b. This is a revised version of paper previously submitted to xxx@lanl.gov. The original version misidentified the Dirichlet and Neumann cases. This version also includes references to work by Yang that was missing in the original.)