Related papers: Boundary operators in minimal Liouville gravity an…
We describe how the matrix integral of Imbimbo and Mukhi arises from a limit of the FZZT partition function in the double-scaled c=1 matrix model. We show a similar result for 0A and comment on subtleties in 0B.
In this paper we study matrix model realizations of Liouville conformal blocks with degenerate and irregular operators. The corresponding matrix model is Hermitian with a $\beta$-deformed measure and the degree of the potential corresponds…
We propose new methods for calculation of the discrete spectrum, the reflection amplitude and the correlation functions of boundary Liouville theory on a strip with Lorentzian signature. They are based on the structure of the vertex…
We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local. We show the…
We investigate the limit of minimal model conformal field theories where the central charge approaches one. We conjecture that this limit is described by a non-rational CFT of central charge one. The limiting theory is different from the…
We continue to study minimal Liouville gravity (MLG) using a dual approach based on the idea that the MLG partition function is related to the tau function of the A_q integrable hierarchy via the resonance transformations, which are in turn…
We consider the boundary WZW model on a half-plane with a cut growing according to the Schramm-Loewner stochastic evolution and the boundary fields inserted at the tip of the cut and at infinity. We study necessary and sufficient conditions…
Liouville field theory approach to 2-dimensional gravity possesses the duality ($b \leftrightarrow b^{-1}$). The matrix counterpart of minimal gravity $\mathcal{M}(q,p)$ ($q<p$ co-prime) is effectively described on $A_{q-1}$ Frobenius…
We establish the first connection between $2d$ Liouville quantum gravity and natural dynamics of random matrices. In particular, we show that if $(U_t)$ is a Brownian motion on the unitary group at equilibrium, then the measures $$…
Previously it was suggested, motivated by correspondence with JT gravity, that tachyon correlators in $(2,2p+1)$ minimal Liouville gravity (MLG) in the $p\to \infty$ (semiclassical) limit should be interpreted as moduli space volumes for…
We propose that the double scaling behavior of the unitary matrix models, and that of the complex matrix models, is related to type 0B and 0A fermionic string theories. The particular backgrounds involved correspond to $\hat c<1 $ matter…
We study canonical quantization of Jackiw-Teibelboim (JT) gravity coupled to a massless scalar field. We provide concrete expressions of matter SL(2,{\,\bf R}) charges and the boundary matter operators in terms of the creation and…
Alday, Gaiotto, and Tachikawa conjectured relations between certain 4d N=2 supersymmetric field theories and 2d Liouville conformal field theory. We study generalizations of these relations to 4d theories with surface operators. For one…
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.…
In critical loop models, we define diagonal boundaries as boundaries that couple to diagonal fields only. Using analytic bootstrap methods, we show that diagonal boundaries are characterised by one complex parameter, analogous to the…
We propose a connection between the newly formulated Virasoro minimal string and the well-established $(2,2m-1)$ minimal string by deriving the string equation of the Virasoro minimal string using the expansion of its density of states in…
We consider the role of boundary conditions in the $AdS_{d+1}/CFT_{d}$ correspondence for the scalar field theory. Also a careful analysis of some limiting cases is presented. We study three possible types of boundary conditions, Dirichlet,…
We study Fateev-Zamolodchikov-Zamolodchikov-Teschner (FZZT) branes in Witten-Kontsevich topological gravity, which includes Jackiw-Teitelboim (JT) gravity as a special case. Adding FZZT branes to topological gravity corresponds to inserting…
We consider the relation of mixed global gauge gravitational anomalies and boundary conformal field theory in WZW models for simple Lie groups. The discrete symmetries of consideration are the centers of the simple Lie groups. These mixed…
We study unitary minimal models coupled to Liouville gravity using Douglas string equation. Our approach is based on the assumption that there exist an appropriate solution of the Douglas string equation and some special choice of the…