Roaming moduli space using dynamical triangulations

TL;DR

This paper introduces a geometric method to assign moduli parameters to triangulations in non-critical string theory, demonstrating convergence of the moduli integrand to known continuum expressions through numerical analysis.

Contribution

It presents a simple geometric approach to assign moduli parameters to dynamical triangulations in non-critical string theory, enabling the construction of the moduli integrand.

Findings

Moduli integrand converges to continuum expression as triangles increase.

Method works for central charges c=0 and c=-2.

Provides numerical evidence supporting the regularization approach.

Abstract

In critical as well as in non-critical string theory the partition function reduces to an integral over moduli space after integration over matter fields. For non-critical string theory this moduli integrand is known for genus one surfaces. The formalism of dynamical triangulations provides us with a regularization of non-critical string theory. We show how to assign in a simple and geometrical way a moduli parameter to each triangulation. After integrating over possible matter fields we can thus construct the moduli integrand. We show numerically for $c=0$ and $c=-2$ non-critical strings that the moduli integrand converges to the known continuum expression when the number of triangles goes to infinity.