The toroidal Hausdorff dimension of 2d Euclidean quantum gravity


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.

Phys. Lett. B 724 (2013) 328-332


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