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

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.

15 pages, 10 figures, LaTeX, JHEP3.cls; references added, typos corrected

References in corpus (10)

• Exact scaling functions for one-dimensional stationary KPZ growth
• Blackhole/String Transition for the Small Schwarzschild Blackhole of $Ad{S}_5\times S^5$ and Critical Unitary Matrix Models
• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• A string field theoretical description of (p,q) minimal superstrings
• Nonperturbative Effect in c=1 Noncritical String Theory and Penner Model
• T-duality of ZZ-brane
• Double Scaling Limits in Gauge Theories and Matrix Models
• Double Scaling Limits and Twisted Non-Critical Superstrings
• Phase structure of the large-N reduced gauge theory and generalized Weingarten model
• Phase transitions of Large-N two-dimensional Yang-Mills and generalized Yang-Mills theories in the double scaling limit

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• Macroscopic loop amplitudes in the multi-cut two-matrix models
• Wilson RG of Noncommutative ${\Phi }_4^4$