Related papers: Two Point Correlation Function of Sine-Liouville T…
We review and study the duality between string theory formulated on a curved exact background (the two dimensional black hole) and string theory in flat space with a tachyon-like potential. We generalize previous results in this subject by…
We study the perturbative S-matrix of closed strings in the two-dimensional type 0B string theory from the worldsheet perspective, by directly integrating correlation functions of ${\cal N}=1$ Liouville theory. The latter is computed…
We propose that there exist generalized Seiberg-Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. These identities involve a…
We study semiclassical correlation functions in Liouville field theory on a two-sphere when all operators have large conformal dimensions. In the usual approach, such computation involves solving the classical Liouville equation, which is…
It is shown that the general 3-point function $<\Phi_{a} \Phi_{b} \Phi_{c}>$, with continuous values of charges $a, b, c$ of a statistical model operators, and the 3-point function of the Liouville model, could all be obtained by successive…
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'…
We present an infinite set of higher equations of motion in N=2 supersymmetric Liouville field theory. They are in one to one correspondence with the degenerate representations and are enumerated in addition to the U(1) charge \omega by the…
In this paper we consider non-relativistic-conformal group, then we calculate two point function for the fields that are Galilean conformal-invariant, then we show that the correlation function for Galilean conformal-invariant fields in…
The purpose of these notes, based on a series of 4 lectures given by the author at IHES, is to explain the recent proof of the DOZZ formula for the three point correlation functions of Liouville conformal field theory (LCFT). We first…
We compute exactly the partition function of two dimensional N=(2,2) gauge theories on S^2 and show that it admits two dual descriptions: either as an integral over the Coulomb branch or as a sum over vortex and anti-vortex excitations on…
We propose a relation between correlation functions in the 2d A_{N-1} conformal Toda theories and the Nekrasov instanton partition functions in certain conformal N=2 SU(N) 4d quiver gauge theories. Our proposal generalises the recently…
The properties of completely degenerate fields in the Conformal Toda Field Theory are studied. It is shown that a generic four-point correlation function that contains only one such field does not satisfy ordinary differential equation in…
We study the non-perturbative corrections (NPC) to the partition function of a compactified 2D string theory in a time-dependent background generated by a tachyon source. The sine-Liouville deformation of the theory is a particular case of…
I study some possibilities of analytically solving a particular Sturm-Liouville problem with step-wise (piece-constant) coefficients with help of an iterative procedure mentioned in my previous paper (Green's function sum rules). I…
We consider the U_qSU(2) invariant spin-1/2 XXZ quantum spin chain at roots of unity q=exp(i*pi/(m+1)), corresponding to different minimal models of conformal field theory. We conduct a numerical investigation of correlation functions of…
Two point correlation functions of the off-critical primary fields \phi_{1, 1+s} are considered in the perturbed minimal models M_{2, 2N+3} + \phi_{1,3}. They are given as infinite series of form factor contributions. The form factors of…
We study the Toda field theory with finite Lie algebras using an extension of the Goulian-Li technique. In this way, we show that, after integrating over the zero mode in the correlation functions of the exponential fields, the resulting…
It is shown that the two dimensional gravity, described either in the conformal gauge (the Liouville theory) or in the light cone gauge, when coupled to matter possesses an infinite number of twisted $N=2$ superconformal symmetries. The…
In critical loop models, there exist diagonal fields with arbitrary conformal dimensions, whose $3$-point functions coincide with those of Liouville theory at $c\leq 1$. We study their $N$-point functions, which depend on the $2^{N-1}$…
We identify the puncture operator in c=1 Liouville gravity as the discrete state with spin J=1/2. The correlation functions involving this operator satisfy the recursion relation which is characteristic in topological gravity. We derive the…