The toroidal Hausdorff dimension of 2d Euclidean quantum gravity

Abstract

The lengths of shortest non-contractible loops are studied numerically in 2d Euclidean quantum gravity on a torus coupled to conformal field theories with central charge less than one. We find that the distribution of these geodesic lengths displays a scaling in agreement with a Hausdorff dimension given by the formula of Y. Watabiki.

13 pages, 4 figures

References in corpus (4)

• Roaming moduli space using dynamical triangulations
• Baby Universes Revisited
• The Hausdorff Dimension of Two-Dimensional Quantum Gravity
• Semi-classical Dynamical Triangulations

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• Pseudo-Cartesian coordinates in a model of Causal Dynamical Triangulations
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• Precision measurements of Hausdorff dimensions in two-dimensional quantum gravity
• The spectral dimension in 2D CDT gravity coupled to scalar fields