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 …
designed to capture the mathematical essence of the Conformal Bootstrap formalism …
Integrability of SLE via conformal welding of random surfaces
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 …
(SLE) from Liouville conformal field theory (LCFT) and the mating‐of‐trees framework for …
FZZ formula of boundary Liouville CFT via conformal welding
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 …
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
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 …
similar growth-fragmentation processes by focusing on martingales which appear naturally …
Conformal welding of quantum disks
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 …
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 …
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 …
complex Lie algebras. They are natural generalizations of the Liouville CFT in that they …
Supercritical Liouville quantum gravity and CLE
We establish the first relationship between Schramm-Loewner evolution (SLE) and Liouville
quantum gravity (LQG) in the supercritical (aka strongly coupled) phase, which corresponds …
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 …
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 …
Conformal Field Theory. As a corollary we present a new derivation of the Belavin-Polyakov …