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.

Comments: 13 pages, 4 figures