The Hausdorff Dimension of Two-Dimensional Quantum Gravity
Mathematical Physics
2011-08-17 v1 math.MP
Probability
Abstract
We argue that the Hausdorff dimension D of a quantum gravity random surface is always D=4, irrespective of the conformal central charge c, c between -2 and 1, of a critical statistical model possibly borne by it. The Knizhnik-Polyakov-Zamolodchikov (KPZ) relation allows one to determine the dimension D from the exact Hausdorff dimension of random maps with large faces, recently rigorously studied by Le Gall and Miermont, and reformulated by Borot, Bouttier and Guitter as a loop model on a random quadrangulation. This contradicts several earlier conjectured formulae for D in terms of c.
Keywords
Cite
@article{arxiv.1108.3327,
title = {The Hausdorff Dimension of Two-Dimensional Quantum Gravity},
author = {Bertrand Duplantier},
journal= {arXiv preprint arXiv:1108.3327},
year = {2011}
}