Related papers: Liouville theory without an action
We construct Euclidean Liouville conformal field theories in odd number of dimensions. The theories are nonlocal and non-unitary with a log-correlated Liouville field, a ${\cal Q}$-curvature background, and an exponential Liouville-type…
We compute the disk 1-point function in timelike Liouville theory. Using the Coulomb gas formalism and analytically continuing in the number of screening operators, we derive an explicit formula, which is shown to satisfy the correct…
The most general vortex solution of the Liouville equation (which arises in non-relativistic Chern-Simons theory) is associated with rational functions, $f(z)=P(z)/Q(z)$ where $P(z)$ and $Q(z)$ are both polynomials, $\deg P<\deg Q\equiv N$.…
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…
Liouville conformal field theory describes a random geometry that fluctuates around a deterministic one: the unique solution of the problem of finding, within a given conformal class, a Riemannian metric with prescribed scalar and geodesic…
We give a short and rigorous proof of the existence and uniqueness of the solution of Liouville equation with sources, both elliptic and parabolic, on the sphere and on all higher genus compact Riemann surfaces.
Liouville (super)integrability of a Hamiltonian system of differential equations is based on the existence of globally well-defined constants of the motion, while Lie point symmetries provide a local approach to conserved integrals.…
We provide a simple method for obtaining new Liouville theorems for scaling invariant superlinear parabolic problems with gradient structure. To illustrate the method we prove Liouville theorems (guaranteeing nonexistence of positive…
We initiate the study of the conformal bootstrap using Sturm-Liouville theory, specializing to four-point functions in one-dimensional CFTs. We do so by decomposing conformal correlators using a basis of eigenfunctions of the Casimir which…
The quantisation of the two-dimensional Liouville field theory is investigated using the path integral, on the sphere, in the large radius limit. The general form of the $N$-point functions of vertex operators is found and the three-point…
A comparison is made between proposals for the exact three point function in Liouville quantum field theory and the nonperturbative weak coupling expansion developed long ago by Braaten, Curtright, Ghandour, and Thorn. Exact agreement to…
We establish a Liouville type theorem for some conformally invariant fully nonlinear equations
In the paper, we review the recent construction of the Liouville conformal field theory (CFT) from probabilistic methods, and the formalization of the conformal bootstrap. This model has offered a fruitful playground to unify the…
We construct topological defects in the Liouville field theory producing jump in the value of cosmological constant. We construct them using the Cardy-Lewellen equation for the two-point function with defect. We show that there are…
Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.
We work out the perturbative expansion of quantum Liouville theory on the pseudosphere starting from the semiclassical limit of a background generated by heavy charges. By solving perturbatively the Riemann-Hilbert problem for the Poincare'…
The paper presents the representation of quantum field theory without introduction of infinity bare masses and coupling constants of fermions. Counter-terms, compensating for divergent quantities in self-energy diagrams of fermions and…
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…
For graphs with non-negative Ollivier curvature, we prove the Liouville property, i.e., every bounded harmonic function is constant. Moreover, we improve Ollivier's results on concentration of the measure under positive Ollivier curvature.
It is shown that, by appropriately defining the eigenfunctions of a function defined on the extended phase space, the Liouville theorem on solutions of the Hamilton--Jacobi equation can be formulated as the problem of finding common…