English
Related papers

Related papers: The SLE Bubble Measure via Conformal Welding of Qu…

200 papers

We prove that SLE$_\kappa$ for $\kappa \in (4,8)$ on an independent $\gamma=4/\sqrt{\kappa}$-Liouville quantum gravity (LQG) surface is uniquely characterized by the form of its LQG boundary length process and the form of the conditional…

Probability · Mathematics 2021-02-12 Ewain Gwynne , Jason Miller

We solve the classical conformal welding problem for a composition of two random homeomorphisms generated by independent Gaussian multiplicative chaos measures with small parameter values. In other words, given two such measures on the…

Probability · Mathematics 2026-01-27 Antti Kupiainen , Michael McAuley , Eero Saksman

Let $Q$ be a free Boltzmann quadrangulation with simple boundary decorated by a critical ($p=3/4$) face percolation configuration. We prove that the chordal percolation exploration path on $Q$ between two marked boundary edges converges in…

Probability · Mathematics 2021-02-12 Ewain Gwynne , Jason Miller

Permutons constructed from a Liouville quantum gravity surface and a pair of space-filling Schramm-Loewner evolutions (SLEs) have been shown -- or are conjectured -- to describe the scaling limit of various natural models of random…

Probability · Mathematics 2024-09-25 Jacopo Borga , Ewain Gwynne

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 depend on the dimensional ratios of boundary…

High Energy Physics - Theory · Physics 2007-05-23 V. Fateev , A. Zamolodchikov , Al. Zamolodchikov

We study a two-dimensional conformal field theory coupled to quantum gravity on a disk. Using the continuum Liouville field approach, we compute three-point correlation functions of boundary operators. The structure of momentum…

High Energy Physics - Theory · Physics 2009-10-22 Yoshiaki Tanii , Shun-ichi Yamaguchi

A Liouville quantum gravity (LQG) surface is a natural random two-dimensional surface, initially formulated as a random measure space and later as a random metric space. We show that the LQG measure can be recovered as the Minkowski measure…

Probability · Mathematics 2023-10-13 Ewain Gwynne , Jinwoo Sung

In this paper we will consider the Almheiri-Polchinski model of the AdS$_2$ back reaction coupled with Liouville field, which is necessary for quantum consistency. In this model, the Liouville field is determined classically by a bulk…

High Energy Physics - Theory · Physics 2019-12-06 Ryuichi Nakayama , Tomotaka Suzuki

There is a simple way to "glue together" a coupled pair of continuum random trees (CRTs) to produce a topological sphere. The sphere comes equipped with a measure and a space-filling curve (which describes the "interface" between the…

Probability · Mathematics 2020-08-20 Bertrand Duplantier , Jason Miller , Scott Sheffield

We study shape deformations of two-dimensional end-of-the-world (ETW) branes, such as those in bottom-up models of two-dimensional holographic boundary conformal field theories (BCFT), and derive an action for the theory of brane…

High Energy Physics - Theory · Physics 2024-04-12 Dominik Neuenfeld , Andrew Svesko , Watse Sybesma

Originating in theoretical physics, Liouville quantum gravity (LQG) has been an important topic in probability theory and mathematical physics in the past two decades. In this proceeding, we review two aspects of this topic. The first is…

Probability · Mathematics 2025-10-21 Nina Holden , Xin Sun

We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle. The homeomorphism is constructed using the exponential of $\beta X$ where $X$ is the restriction of the…

Complex Variables · Mathematics 2009-09-08 K. Astala , P. Jones , A. Kupiainen , E. Saksman

We consider a particular type of $\sqrt{8/3}$-Liouville quantum gravity surface called a doubly marked quantum disk (equivalently, a Brownian disk) decorated by an independent chordal SLE$_6$ curve $\eta$ between its marked boundary points.…

Probability · Mathematics 2018-07-03 Ewain Gwynne , Jason Miller

We obtain exact formulae for three basic quantities in random conformal geometry that depend on the modulus of an annulus. The first is for the law of the modulus of the Brownian annulus describing the scaling limit of uniformly sampled…

Probability · Mathematics 2025-02-18 Morris Ang , Guillaume Remy , Xin Sun

Previous works in this series have shown that an instance of a $\sqrt{8/3}$-Liouville quantum gravity (LQG) sphere has a well-defined distance function, and that the resulting metric measure space (mm-space) agrees in law with the Brownian…

Probability · Mathematics 2020-11-23 Jason Miller , Scott Sheffield

Three-dimensional gauge theory T[G] arises on a domain wall between four-dimensional N=4 SYM theories with the gauge groups G and its S-dual G^L. We argue that the N=2^* mass deformation of the bulk theory induces a mass-deformation of the…

High Energy Physics - Theory · Physics 2011-01-04 Kazuo Hosomichi , Sungjay Lee , Jaemo Park

The timelike boundary Liouville (TBL) conformal field theory consisting of a negative norm boson with an exponential boundary interaction is considered. TBL and its close cousin, a positive norm boson with a non-hermitian boundary…

High Energy Physics - Theory · Physics 2009-09-17 M. Gutperle , A. Strominger

Motivated by the recent work on $T\bar{T}$-type deformations of 2D CFTs, a especial class of single-trace deformations of AdS$_3$/CFT$_2$ correspondence has been investigated. From the worldsheet perspective, this corresponds to a marginal…

High Energy Physics - Theory · Physics 2020-05-20 Gaston Giribet , Matias Leoni

Liouville field theory on the pseudosphere is considered (Dirichlet conditions). We compute explicitely the bulk-boundary structure constant with two different methods: first we use a suggestion made by Hosomichi in JHEP 0111 (2001) that…

High Energy Physics - Theory · Physics 2009-11-10 Benedicte Ponsot

A large class of Jordan curves on the Riemann sphere can be encoded by circle homeomorphisms via conformal welding, among which we consider the welding homeomorphism of the random SLE loops and the Weil-Petersson class of quasicircles. It…

Probability · Mathematics 2025-02-24 Shuo Fan , Jinwoo Sung