Related papers: Boundary Liouville Theory and 2D Quantum Gravity
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…
Quantization of two-dimensional dilaton gravity coupled to conformal matter is investigated. Working in conformal gauge about a fixed background metric, the theory may be viewed as a sigma model whose target space is parameterized by the…
Within the path integral formalism, we compute the disk partition functions of two dimensional Liouville and JT quantum gravity theories coupled to a matter CFT of central charge $c$, with cosmological constant $\Lambda$, in the limit…
We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a…
Liouville field theory has long been a cornerstone of two-dimensional quantum field theory and quantum gravity, which has attracted much recent attention in the mathematics literature. Timelike Liouville field theory is a version of…
We study the quantum aspects of the conformal gravity in four dimensions, specifically addressing a known discrepancy in beta functions between general quadratic curvature theories and conformal gravity, which corresponds to two scalar…
We develop a perturbative expansion of quantum Liouville theory on the pseudosphere around the background generated by heavy charges. Explicit results are presented for the one and two point functions corresponding to the summation of…
For Brownian surfaces with boundary and an interior marked point, a natural observable to consider is the distance profile, defined as the process of distances from the marked point to a variable point $x$ lying on the boundary. When the…
Our purpose is to pursue the rigorous construction of Liouville Quantum Field Theory on Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context of the Riemann sphere and inspired by the 1981 seminal work…
We define a three-parameter family of random surfaces in Liouville quantum gravity (LQG) which can be viewed as the quantum version of triangles. These quantum triangles are natural in two senses. First, by our definition they produce the…
The theory of the 2-dimensional Liouville Quantum Gravity, first introduced by Polyakov in his 1981 work has become a key notion in the study of random surfaces. In a series of articles, David, Huang, Kupiainen, Rhodes and Vargas, on the…
We define a three-dimensional quantum theory of gravity as the holographic dual of the Liouville conformal field theory. The theory is consistent and unitary by definition. The corresponding theory of gravity with negative cosmological…
Quantum mechanical boundary conditions along a timelike line, corresponding to the origin in radial coordinates, in two-dimensional dilaton gravity coupled to $N$ matter fields, are considered. Conformal invariance and vacuum stability…
We prove that the probabilistic definition of the most general boundary three-point and bulk-boundary structure constants in Liouville conformal field theory (LCFT) agree respectively with the formula proposed by Ponsot-Techsner (2002) and…
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-Zamolodchikov differential equations. Our method of proof…
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
In this paper, we construct the Brownian motion of Liouville Quantum Gravity with central charge $c=1$ (more precisely we restrict to the corresponding free field theory). Liouville quantum gravity with $c=1$ corresponds to two-dimensional…
The nonlinear structures in 2D quantum gravity coupled to the $(q+1,q)$ minimal model are studied in the Liouville theory to clarify the factorization and the physical states. It is confirmed that the dressed primary states outside the…
The theory of embedded random surfaces, equivalent to two--dimensional quantum gravity coupled to matter, is reviewed, further developed and partly generalized to four dimensions. It is shown that the action of the Liouville field theory…
We give a concise presentation of the construction of the Liouville quantum gravity (LQG) eigenvalues and eigenfunctions, i.e., the spectrum associated to the infinitesimal generator of Liouville Brownian motion, the canonical diffusion in…