Geodesic distances in Liouville quantum gravity

Nuclear Physics B. 2014;889(C):676-691 DOI 10.1016/j.nuclphysb.2014.10.029

 

Journal Homepage

Journal Title: Nuclear Physics B

ISSN: 0550-3213 (Print); 1873-1562 (Online)

Publisher: Elsevier

LCC Subject Category: Science: Physics: Nuclear and particle physics. Atomic energy. Radioactivity

Country of publisher: Netherlands

Language of fulltext: English

Full-text formats available: PDF, HTML

 

AUTHORS

J. Ambjørn (The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark)
T.G. Budd (The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark)

EDITORIAL INFORMATION

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Time From Submission to Publication: 12 weeks

 

Abstract | Full Text

In order to study the quantum geometry of random surfaces in Liouville gravity, we propose a definition of geodesic distance associated to a Gaussian free field on a regular lattice. This geodesic distance is used to numerically determine the Hausdorff dimension associated to shortest cycles of 2d quantum gravity on the torus coupled to conformal matter fields, showing agreement with a conjectured formula by Y. Watabiki. Finally, the numerical tools are put to test by quantitatively comparing the distribution of lengths of shortest cycles to the corresponding distribution in large random triangulations.