相关论文: On fusion kernel in Liouville theory
We investigate the initial-value problem of the non-linear Liouville hierarchy. For the general form of the interaction potential we construct an explicit solution in terms of an expansion over particle clusters whose evolution is described…
General properties of perturbed conformal field theory interacting with quantized Liouville gravity are considered in the simplest case of spherical topology. We discuss both short distance and large distance asymptotic of the partition…
We develop a general technique for computing functional integrals with fixed area and boundary length constraints. The correct quantum dimensions for the vertex functions are recovered by properly regularizing the Green function. Explicit…
We find a formula for the Virasoro fusion kernel at $c=25$, in terms of the connection coefficients of the Painlev\'e VI differential equation. Our formula agrees numerically with previously known integral representations of the kernel. The…
In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation \begin{equation*} u(x)=\overrightarrow{l}+C_*\int_{\mathbb{R}^{n}}\frac{u(1-|u|^{2})}{|x-y|^{n-\alpha}}dy. \end{equation*} Here $u:…
This paper addresses the problem of finding an asymptotic solution for first and second order integro-differential equations containing an arbitrary kernel, by evaluating the corresponding inverse Laplace and Fourier transforms. The aim of…
The defects and permutation branes for the Liouville field theory are considered. By exploiting cluster condition, equations satisfied by permutation branes and defects reflection amplitudes are obtained. It is shown that two types of…
In this paper, a temporal nonuniform $L1$ type difference scheme is built up for the time fractional diffusion-wave equation with the help of the order reduction technique. The unconditional convergence of the nonuniform difference scheme…
In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation has a stronger non-local feature and is not the dual of any PDE. We obtain the existence of…
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel…
We initiate in this paper the study of analytic properties of the Liouville heat kernel. In particular, we establish regularity estimates on the heat kernel and derive non trivial lower and upper bounds.
Let $A=(a_{ij})_{n\times n}$ be a nonnegative, symmetric, irreducible and invertible matrix. We prove the existence and uniqueness of radial solutions to the following Liouville system with singularity: $$\{{array}{ll} \Delta…
Liouville theorems for scaling invariant nonlinear parabolic equations and systems (saying that the equation or system does not possess positive entire solutions) guarantee optimal universal estimates of solutions of related initial and…
We establish Liouville type theorems for degenerate conformally invariant equations.
We derive and solve the difference equations on the toric modular kernel following from the consistency relations in the fusion algebra. The result is explicit and simple series expansion for the toric modular kernel of non-degenerate…
The continuation of the Liouville conformal field theory to c<=1 is considered. The viability of an interpretation involving a timelike boson which is the conformal factor for two-dimensional asymptotically de Sitter geometries is examined.…
We establish a reduction principle to derive Li-Yau inequalities for non-local diffusion problems in a very general framework, which covers both the discrete and continuous setting. Our approach is not based on curvature-dimension…
The rich phenomenology of collective neutrino oscillations has been studied only in one-dimensional or spherically symmetric systems. Motivated by the non-spherical example of coalescing neutron stars, presumably the central engines of…
We derive differential equations for multiplicative statistics of the Bessel determinantal point process depending on two parameters. In particular, we prove that such statistics are solutions to an integrable nonlinear partial differential…
In the quantum Teichmuller theory, based on Penner coordinates, the mapping class groups of punctured surfaces are represented projectively. The case of a genus three surface with one puncture is worked out explicitly. The projective factor…