Related papers: Liouville Perturbation Theory
We develop a general technique for solving the Riemann-Hilbert problem in presence of a number of heavy charges and a small one thus providing the exact Green functions of Liouville theory for various non trivial backgrounds. The non…
Reordering of the chiral perturbation series, proposed recently by Becher and Leutwyler in the framework of SU(2) baryonic ChPT, is applied to the SU(3) case. This results in improved convergence of the chiral expansion of static properties…
The production of o(1/g^2) particles in a weakly-coupled theory is believed to be non-perturbatively suppressed. I comment on the prospects of (a) establishing this rigorously, and (b) estimating the effect to exponential accuracy…
Quantum Liouville theory is analyzed in terms of the infinite dimensional representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this…
We have studied the quantum Liouville theory on the Riemann sphere with n>3 punctures. While considering the theory on the Riemann surfaces with n=4 punctures, the quantum theory near an arbitrary but fixed puncture can be obtained via…
We try to develop a coherent picture on Liouville theory as a two-dimensional conformal field theory that takes into account the perspectives of path-integral approach, bootstrap, canonical quantization and operator approach. To do this, we…
We solve the Riemann-Hilbert problem on the sphere topology for three singularities of finite strength and a fourth one infinitesimal, by determining perturbatively the Poincare' accessory parameters. In this way we compute the…
An analytic expression is proposed for the three-point function of the exponential fields in the Liouville field theory on a sphere. In the classical limit it coincides with what the classical Liouville theory predicts. Using this function…
A Liouville function is a complex analytic function H with a Taylor series \sum_{n=1}^{\infty} x^n/a_n such the a_n's form a ``very fast growing'' sequence of integers. In this paper we exhibit the complete first-order theory of the complex…
We study four-point correlation functions with logarithmic behaviour in Liouville field theory on a sphere, which consist of one kind of the local operators. We study them as non-integrated correlation functions of the gravitational sector…
A non-perturbative method which can go beyond the weak coupling perturbation theory is introduced. Essential idea is to formulate a set of exact differential equations as a function of the coupling strength $g$. Unlike other resummation in…
The `strong-coupling' perturbation theory over the inverse interaction constant $1/g$ near the nontrivial solution of Lagrange equation is formulated. The ordinary `week-coupling' perturbation theory over $g$ is described also to compare…
We show that the crossing symmetry of the four-point function in the Liouville conformal field theory on the sphere contains more information than what was hitherto considered. Under certain assumptions, it provides the special structure…
We present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for…
An infinite set of operator-valued relations in Liouville field theory is established. These relations are enumerated by a pair of positive integers $(m,n)$, the first $(1,1)$ representative being the usual Liouville equation of motion. The…
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…
We discuss some physical aspects of our Liouville approach to non-critical strings, including the emergence of a microscopic arrow of time, effective field theories as classical ``pointer'' states in theory space, $CPT$ violation and the…
This work is devoted to the study of a Liouville comparison principle for entire weak solutions of quasilinear differential inequalities of the form $A(u) + |u|^{q-1}u \leq A(v) + |v|^{q-1}v$ on ${\Bbb R}^n$, where $n\geq 1$, $q$ is…
The bootstrap for Liouville theory with conformally invariant boundary conditions will be discussed. After reviewing some results on one- and boundary two-point functions we discuss some analogue of the Cardy condition linking these data.…
We obtain a new Liouville comparison principle for entire weak solutions $(u,v)$ of semilinear parabolic second-order partial differential inequalities of the form $$ u_t -{\mathcal L}u- |u|^{q-1}u\geq v_t -{\mathcal L}v- |v|^{q-1}v (*) $$…