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arXiv · 1108.3327

The Hausdorff Dimension of Two-Dimensional Quantum Gravity

Bertrand Duplantier
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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.

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Bertrand Duplantier. 2011-08-16. The Hausdorff Dimension of Two-Dimensional Quantum Gravity. https://arxiv.org/abs/1108.3327

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