Roaming moduli space using dynamical triangulations

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.

arXiv comment32 pages, many (nice) figures

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• Quantum Flatness in Two-Dimensional CDT Quantum Gravity
• Pseudo-Cartesian coordinates in a model of Causal Dynamical Triangulations
• The toroidal Hausdorff dimension of 2d Euclidean quantum gravity
• Gauge Invariant Computable Quantities In Timelike Liouville Theory
• Properties of dynamical fractal geometries in the model of Causal Dynamical Triangulations
• Semi-classical Dynamical Triangulations
• Phases of Tree-decorated Dynamical Triangulations in 3D