Guillaume Baverez
Fusion asymptotics for Liouville correlation functions
Baverez, Guillaume; Wong, Mo Dick
Abstract
In [DKRV17a], David-Kupiainen-Rhodes-Vargas introduced a probabilistic framework based on the Gaussian Free Field and Gaussian Multiplicative Chaos in order to make sense rigorously of the path integral approach to Liouville Conformal Field Theory (LCFT). We use this setting to compute fusion estimates for the four-point correlation function on the Riemann sphere, and find that it is consistent with predictions from the framework of theoretical physics known as the conformal bootstrap. This result fits naturally into the famous KPZ conjecture [KPZ88] which relates the four-point function to the expected density of points around the root of a large random planar map weighted by some statistical mechanics model. From a purely probabilistic point of view, we give non-trivial results on negative moments of GMC. We give exact formulae based on the DOZZ formula in the Liouville case and asymptotic behaviours in the other cases, with a probabilistic representation of the limit. Finally, we show how to extend our results to boundary LCFT, treating the cases of the fusion of two boundary or bulk insertions as well as the absorption of a bulk insertion on the boundary.
Citation
Baverez, G., & Wong, M. D. (in press). Fusion asymptotics for Liouville correlation functions. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques,
Journal Article Type | Article |
---|---|
Acceptance Date | Mar 4, 2024 |
Deposit Date | May 15, 2024 |
Journal | Annales de l'Institut Henri Poincaré, Probabilités et Statistiques |
Print ISSN | 0246-0203 |
Publisher | Institute Henri Poincaré |
Peer Reviewed | Peer Reviewed |
Public URL | https://durham-repository.worktribe.com/output/2440140 |
Publisher URL | https://imstat.org/journals-and-publications/annales-de-linstitut-henri-poincare/annales-de-linstitut-henri-poincare-accepted-papers/ |
This file is under embargo due to copyright reasons.
You might also like
On Erdős sums of almost primes
(2024)
Journal Article
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search