Related papers: The null identities for boundary operators in the …
In this paper we use recent results on resonance relations between the matrix models and the minimal Liouville gravity to compute the torus correlation numbers in (3,p) minimal Liouville gravity. Namely, we calculate the torus generating…
We continue the study of 2D gravity -- ``matrix model'' duality on the example of $(2,2p+1)$ minimal string. We propose a reformulation of the duality, related to a more conventional one by ``$x-y$ swap'' in the language of topological…
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…
The Liouville approach is applied to the quantum treatment of the dilaton gravity in two dimensions. The physical states are obtained from the BRST cohomology and correlation functions are computed up to three-point functions. For the $N=0$…
We investigate the Ward identities of the $W_{\infty}$ symmetry in the Liouville theory coupled to the $(p,q)$ conformal matter. The correlation functions are defined by applying the analytic continuation procedure for the matter sector as…
We continue the study of $(q,p)$ Minimal Liouville Gravity with the help of Douglas string equation. We generalize the results of \cite{Moore:1991ir}, \cite{Belavin:2008kv}, where Lee-Yang series $(2,2s+1)$ was studied, to $(3,3s+p_0)$…
We consider the two-point functions of conserved bulk currents and energy-momentum tensor in a boundary CFT defined on $\mathbb{R}_-^{1,2}$. Starting from the consistent forms of boundary gauge and gravitational anomalies we derive their…
We evaluate one-point correlation numbers on the torus in the Liouville theory coupled to the conformal matter M(2,2p+1). We find agreement with the recent results obtained in the matrix model approach.
The c=1 Liouville theory has received some attention recently as the Euclidean version of an exact rolling tachyon background. In an earlier paper it was shown that the bulk theory can be identified with the interacting c=1 limit of unitary…
The timelike boundary Liouville (TBL) conformal field theory consisting of a negative norm boson with an exponential boundary interaction is considered. TBL and its close cousin, a positive norm boson with a non-hermitian boundary…
In this paper, we prove that the oscillation operator, variation operator and maximal differential transform associated with the approximate identities are bounded from ${\rm BMO}({\mathbb R}^n)$ to its subspace ${\rm BLO}({\mathbb R}^n)$.
We consider the M(2,3) Minimal Liouville gravity, whose states in the gravity sector are represented by irreducible modules of the Virasoro algebra. We present a recursive construction for BRST cohomology classes. This construction is based…
In asymptotically anti-de Sitter gravity, diffeomorphisms that change the conformal boundary data can be promoted to genuine physical degrees of freedom. I show that in 2+1 dimensions, the dynamics of these degrees of freedom is described…
The tree-level three-point correlation functions of local operators in the general $(p,q)$ minimal models coupled to gravity are calculated in the continuum approach. On one hand, the result agrees with the unitary series ($q=p+1$); and on…
We continue the study of boundary operators in the dense O(n) model on the random lattice. The conformal dimension of boundary operators inserted between two JS boundaries of different weight is derived from the matrix model description.…
The 2D quantum gravity on a disc, or the non-critical theory of open strings, is known to exhibit an integrable structure, the boundary ground ring, which determines completely the boundary correlation functions. Inspired by the recent…
Calder\'on-Zygmund operators with noncommuting kernels may fail to be Lp-bounded for $p \neq 2$, even for kernels with good size and smoothness properties. Matrix-valued paraproducts, Fourier multipliers on group vNa's or noncommutative…
We study a two-dimensional conformal field theory coupled to quantum gravity on a disk. Using the continuum Liouville field approach, we compute three-point correlation functions of boundary operators. The structure of momentum…
In this article, we will show how to use Zamolodchikov's higher equations of motion in Liouville field theory to explicitly calculate $N$-point correlation numbers in minimal Liouville gravity for $N>4$. We find the explicit expression for…
The F and B matrices associated with Virasoro null vectors are derived in closed form by making use of the operator-approach suggested by the Liouville theory, where the quantum-group symmetry is explicit. It is found that the entries of…