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

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

2007-03-23

arxiv.org/abs/hep-th/0703209v2

JHEP 0706:076,2007

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/1126-6708/2007/06/076

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.

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