Large Strebel Graphs and (3,2) Liouville CFT

2D quantum gravity is the idea that a set of discretized surfaces (called map, a graph on a surface), equipped with a graph measure, converges in the large size limit (large number of faces) to a conformal field theory (CFT), and in the simplest case to the simplest CFT known as pure gravity, also k...

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Bibliographic Details
Published in:Annales Henri Poincaré 2018-06, Vol.19 (6), p.1611-1645
Main Authors: Charbonnier, Séverin, Eynard, Bertrand, David, François
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Convergence
Dynamical Systems and Ergodic Theory
Elementary Particles
Field theory
Graphs
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum gravity
Quantum Physics
Relativity Theory
Theoretical
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Summary:2D quantum gravity is the idea that a set of discretized surfaces (called map, a graph on a surface), equipped with a graph measure, converges in the large size limit (large number of faces) to a conformal field theory (CFT), and in the simplest case to the simplest CFT known as pure gravity, also known as the gravity dressed (3,2) minimal model. Here, we consider the set of planar Strebel graphs (planar trivalent metric graphs) with fixed perimeter faces, with the measure product of Lebesgue measure of all edge lengths, submitted to the perimeter constraints. We prove that expectation values of a large class of observables indeed converge toward the CFT amplitudes of the (3,2) minimal model.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-018-0662-x