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

Naoyuki Kawahara·Jun Nishimura·Atsushi Yamaguchi
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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.

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Naoyuki Kawahara, Jun Nishimura, Atsushi Yamaguchi. 2007-05-23. Monte Carlo approach to nonperturbative strings -- demonstration in noncritical string theory. https://doi.org/10.1088/1126-6708%2F2007%2F06%2F076

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