# Integrability of boundary Liouville conformal field theory

@article{Remy2020IntegrabilityOB, title={Integrability of boundary Liouville conformal field theory}, author={Guillaume Remy and Tunan Zhu}, journal={arXiv: Probability}, year={2020} }

Liouville conformal field theory (LCFT) is considered on a simply connected domain with boundary, specializing to the case where the Liouville potential is integrated only over the boundary of the domain. We work in the probabilistic framework of boundary LCFT introduced by Huang-Rhodes-Vargas (2015). Building upon the known proof of the bulk one-point function by the first author, exact formulas are rigorously derived for the remaining basic correlation functions of the theory, i.e., the bulk…

## Figures from this paper

## 8 Citations

Probabilistic conformal blocks for Liouville CFT on the torus

- Mathematics
- 2020

Liouville theory is a fundamental example of a conformal field theory (CFT) first introduced by Polyakov in the context of string theory. Conformal blocks are objects underlying the integrable…

Conformal welding of quantum disks

- Physics
- 2020

Two-pointed quantum disks are a family of finite-area random surfaces that arise naturally in Liouville quantum gravity. In this paper we show that conformally welding two quantum disks according to…

A family of probability distributions consistent with the DOZZ formula: towards a conjecture for the law of 2D GMC

- MathematicsProbability and Mathematical Physics
- 2021

A three parameter family of probability distributions is constructed such that its Mellin transform is defined over the same domain as the 2D GMC on the Riemann sphere with three insertion points…

Integrability of SLE via conformal welding of random surfaces

- Mathematics
- 2021

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 Liouville quantum gravity…

FZZ formula of boundary Liouville CFT via conformal welding

- Mathematics
- 2021

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 disk topology. Fateev,…

The SLE loop via conformal welding of quantum disks

- Mathematics
- 2022

. We prove that the SLE loop measure arises naturally from the conformal welding of two Liouville quantum gravity (LQG) disks for γ 2 = κ ∈ (0 , 4). The proof relies on our companion work on…

What is a random surface?

- Mathematics
- 2022

Given 2n unit equilateral triangles, there are finitely many ways to glue each edge to a partner. We obtain a random sphere-homeomorphic surface by sampling uniformly from the gluings that produce a…

On the Critical–Subcritical Moments of Moments of Random Characteristic Polynomials: A GMC Perspective

- MathematicsCommunications in Mathematical Physics
- 2022

We study the ‘critical moments’ of subcritical Gaussian multiplicative chaos (GMCs) in dimensions $$d \le 2$$
d
≤
2
. In particular, we establish a fully explicit formula for the leading…

## References

SHOWING 1-10 OF 35 REFERENCES

Boundary Liouville Field Theory I. Boundary State and Boundary Two-point Function

- Mathematics, Physics
- 2000

Liouville conformal field theory is considered with conformal boundary. There is a family of conformal boundary conditions parameterized by the boundary cosmological constant, so that observables…

The Fyodorov–Bouchaud formula and Liouville conformal field theory

- MathematicsDuke Mathematical Journal
- 2020

In a remarkable paper in 2008, Fyodorov and Bouchaud conjectured an exact formula for the density of the total mass of (sub-critical) Gaussian multiplicative chaos (GMC) associated to the Gaussian…

Liouville quantum gravity on the annulus

- MathematicsJournal of Mathematical Physics
- 2018

In this work we construct Liouville quantum gravity on an annulus in the complex plane. This construction is aimed at providing a rigorous mathematical framework to the work of theoretical physicists…

Local Conformal Structure of Liouville Quantum Gravity

- MathematicsCommunications in Mathematical Physics
- 2018

In 1983 Belavin, Polyakov, and Zamolodchikov (BPZ) formulated the concept of local conformal symmetry in two dimensional quantum field theories. Their ideas had a tremendous impact in physics and…

Integrability of Liouville theory: proof of the DOZZ formula

- Mathematics
- 2017

Dorn and Otto (1994) and independently Zamolodchikov and Zamolodchikov (1996) proposed a remarkable explicit expression, the so-called DOZZ formula, for the 3 point structure constants of Liouville…

Liouville Field Theory — A decade after the revolution

- Physics
- 2004

We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of three parts. In part I, we review the bosonic Liouville theory.…

Liouville quantum gravity on complex tori

- Mathematics
- 2016

In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov [Phys. Lett. B 103, 207 (1981)]. Our approach follows the…

The distribution of Gaussian multiplicative chaos on the unit interval

- MathematicsThe Annals of Probability
- 2020

We consider the sub-critical Gaussian multiplicative chaos (GMC) measure defined on the unit interval [0,1] and prove an exact formula for the fractional moments of the total mass of this measure.…