Monte Carlo approach to nonperturbative strings -- demonstration in noncritical string theory

TL;DR

This paper demonstrates how Monte Carlo methods can effectively study the double scaling limit in matrix models, providing a constructive approach to noncritical string theory with worldsheet supersymmetry.

Contribution

It introduces a Monte Carlo approach to analyze the double scaling limit in a solvable hermitian one-matrix model relevant to noncritical string theory.

Findings

Clear scaling behavior observed in data from matrix sizes 8 to 512

Accurate extraction of the double scaling limit

Specific heat matches known Painleve-II solutions

Abstract

We show how Monte Carlo approach can be used to study the double scaling limit in matrix models. As an example, we study a solvable hermitian one-matrix model with the double-well potential, which has been identified recently as a dual description of noncritical string theory with worldsheet supersymmetry. This identification utilizes the nonperturbatively stable vacuum unlike its bosonic counterparts, and therefore it provides a complete constructive formulation of string theory. Our data with the matrix size ranging from 8 to 512 show a clear scaling behavior, which enables us to extract the double scaling limit accurately. The ``specific heat'' obtained in this way agrees nicely with the known result obtained by solving the Painleve-II equation with appropriate boundary conditions.