Segal's axioms and bootstrap for Liouville Theory

C Guillarmou, A Kupiainen, R Rhodes… - arXiv preprint arXiv …, 2021 - arxiv.org
In 1987 Graeme Segal gave a functorial definition of Conformal Field Theory (CFT) that was
designed to capture the mathematical essence of the Conformal Bootstrap formalism …

Integrability of SLE via conformal welding of random surfaces

M Ang, N Holden, X Sun - Communications on Pure and …, 2024 - Wiley Online Library
We demonstrate how to obtain integrability results for the Schramm‐Loewner evolution
(SLE) from Liouville conformal field theory (LCFT) and the mating‐of‐trees framework for …

FZZ formula of boundary Liouville CFT via conformal welding

M Ang, G Remy, X Sun - Journal of the European Mathematical Society, 2023 - ems.press
Abstract Liouville Conformal Field Theory (LCFT) on the disk describes the conformal factor
of the quantum disk, which is the natural random surface in Liouville quantum gravity with …

Martingales in self-similar growth-fragmentations and their connections with random planar maps

J Bertoin, T Budd, N Curien, I Kortchemski - Probability Theory and …, 2018 - Springer
The purpose of the present work is twofold. First, we develop the theory of general self-
similar growth-fragmentation processes by focusing on martingales which appear naturally …

Conformal welding of quantum disks

M Ang, N Holden, X Sun - Electronic Journal of Probability, 2023 - projecteuclid.org
Two-pointed quantum disks with a weight parameter W> 0 are a family of finite-area random
surfaces that arise naturally in Liouville quantum gravity. In this paper we show that …

[图书][B] Random surfaces: large deviations principles and gradient Gibbs measure classifications

SR Sheffield - 2003 - search.proquest.com
We study (discretized)“random surfaces,” which are random functions from [special
characters omitted](or large subsets of [special characters omitted]) to either [special …

Three-point correlation functions in the Toda theory I: reflection coefficients

B Cerclé - Probability Theory and Related Fields, 2024 - Springer
Toda conformal field theories (CFTs) form a family of 2d CFTs indexed by semisimple and
complex Lie algebras. They are natural generalizations of the Liouville CFT in that they …

Supercritical Liouville quantum gravity and CLE

M Ang, E Gwynne - arXiv preprint arXiv:2308.11832, 2023 - arxiv.org
We establish the first relationship between Schramm-Loewner evolution (SLE) and Liouville
quantum gravity (LQG) in the supercritical (aka strongly coupled) phase, which corresponds …

Compactified Imaginary Liouville Theory

C Guillarmou, A Kupiainen, R Rhodes - arXiv preprint arXiv:2310.18226, 2023 - arxiv.org
On a given Riemann surface, we construct a path integral based on the Liouville action
functional with imaginary parameters. The construction relies on the compactified Gaussian …

Higher equations of motion for boundary Liouville Conformal Field Theory from the Ward identities

B Cerclé - arXiv preprint arXiv:2401.13271, 2024 - arxiv.org
In this document we prove higher equations of motion at the level $2 $ for boundary Liouville
Conformal Field Theory. As a corollary we present a new derivation of the Belavin-Polyakov …