Large Strebel Graphs and (3,2) Liouville CFT

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 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annales Henri Poincaré Springer Journals

Large Strebel Graphs and (3,2) Liouville CFT

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Physics; Theoretical, Mathematical and Computational Physics; Dynamical Systems and Ergodic Theory; Quantum Physics; Mathematical Methods in Physics; Classical and Quantum Gravitation, Relativity Theory; Elementary Particles, Quantum Field Theory
ISSN
1424-0637
eISSN
1424-0661
D.O.I.
10.1007/s00023-018-0662-x
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Annales Henri PoincaréSpringer Journals

Published: Mar 24, 2018

References

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