Related papers: On the Three-point Function in Minimal Liouville G…
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 remind the definition and main properties of the Krichever quasiclassical tau-function, and turn to the application of these formulas for recent studies of two-dimensional quantum gravity. We show, that in the case of minimal gravity it…
We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one…
Structure constants of minimal conformal theories are reconsidered. It is shown that {\it ratios} of structure constants of spin zero fields of a non-diagonal theory over the same evaluated in the diagonal theory are given by a simple…
We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a…
Two-point correlation functions of spin operators in the minimal models ${{\cal M}}_{p,p'}$ perturbed by the field $\Phi_{13}$ are studied in the framework of conformal perturbation theory. The first-order corrections for the structure…
We use the connection between the Frobrenius manifold and the Douglas string equation to further investigate Minimal Liouville gravity. We search a solution of the Douglas string equation and simultaneously a proper transformation from the…
It is well known that string theory can be formulated as two dimensional gravity coupled to matter. In the 2d gravity formulation the central charge of the matter together with a hidden dimension from the conformal factor or Liouville mode…
We study conformal twist field four-point functions on a $\mathbb Z_N$ orbifold. We examine in detail the case $N=3$ and analyze theories obtained by replicated $N$-times a minimal model with central charge $c<1$. A fastly convergent…
We compute the correlation functions of irregular Gaiotto states appearing in the colliding limit of the Liouville theory by using "regularizing" conformal transformations mapping the irregular (coherent) states to regular vertex operators…
The recently proposed expression for the general three point function of exponential fields in quantum Liouville theory on the sphere is considered. By exploiting locality or crossing symmetry in the case of those four-point functions,…
The conformal symmetry in the Liouville theory is analysed by using the Hamiltonian light--front formalism. The boundary conditions of dynamical variables are seen to involve an arbitrary function of time, so that the standard methods for…
We compute the three-point structure constants for short primary operators of N=4 super Yang-Mills theory to leading order in the inverse coupling by mapping the problem to a flat-space string theory calculation. We check the validity of…
We present a systematic small-$b$ expansion of the Liouville DOZZ three-point structure constant in the light-operator regime \(\alpha_i=b\sigma_i\) as \(b\to0\). In this limit, the exact DOZZ function factorizes into a prefactor \({\cal…
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…
We discuss the geometry behind some integrals related to structure constants of the Liouville conformal field theory.
In logarithmic conformal field theory, primary fields come together with logarithmic partner fields on which the stress-energy tensor acts non-diagonally. Exploiting this fact and global conformal invariance of two- and three-point…
In this note, we continue our study of Liouville theory and celestial amplitudes by deriving a set of partial differential equations governing the $n$-point MHV celestial amplitudes for gluons and gravitons, parametrised by the Liouville…
We discuss conserved currents and operator product expansions (OPE's) in the context of a $O(N)$ invariant conformal field theory. Using OPE's we find explicit expressions for the first few terms in suitable short-distance limits for…
Let $\Sigma$ be a complete Riemannian manifold with the volume doubling property and the uniform Neumann-Poincar$\mathrm{\acute{e}}$ inequality. We show that any positive minimal graphic function on $\Sigma$ is a constant.