相关论文: Higher Equations of Motion in Boundary Liouville F…
Similarly to the ordinary bosonic Liouville field theory, in its N=1 supersymmetric version an infinite set of operator valued relations, the ``higher equations of motions'', holds. Equations are in one to one correspondence with the…
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…
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…
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…
Higher dimensional Euclidean Liouville conformal field theories (LCFTs) consist of a log-correlated real scalar field with a background charge and an exponential potential. We analyse the LCFT on a four-dimensional manifold with a boundary.…
In this document we prove higher equations of motion at the level 2 for boundary Liouville Conformal Field Theory. As a corollary we present a new derivation of the Belavin-Polyakov-Zamolodchikov differential equations. Our method of proof…
Liouville field theory is considered on domains with conformally invariant boundary conditions. We present an explicit expression for the three point function of boundary fields in terms of the fusion coefficients which determine the…
We study the boundary correlation functions in Liouville theory and in solvable statistical models of 2D quantum gravity. In Liouville theory we derive functional identities for all fundamental boundary structure constants, similar to the…
We develop a general technique for computing functional integrals with fixed area and boundary length constraints. The correct quantum dimensions for the vertex functions are recovered by properly regularizing the Green function. Explicit…
The Ward identities of the Liouville gravity coupled to the minimal conformal matter are investigated. We introduce the pseudo-null fields and the generalized equations of motion, which are classified into series of the Liouville charges.…
A recursive formula for an infinity of integrals of motion for the super-Liouville theory is derived. The integrable boundary interactions for this theory and the super-Toda theory based on the affine superalgebra $B^{(1)} (0,1)$ are…
We prove conjectures of Zamolodchikov and Belavin-Belavin in Liouville conformal field theory (CFT), which are generalisations of the celebrated Belavin-Polyakov-Zamolodchikov equations known as the higher equations of motion.…
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 one matrix model is known to reproduce in the continuum limit the (2,2p+1) minimal Liouville gravity. Recently, two of the authors have shown how to construct arbitrary critical boundary conditions within this matrix model. So far,…
Liouville field theory is considered with boundary conditions corresponding to a quantization of the classical Lobachevskiy plane (i.e. euclidean version of $AdS_2$). We solve the bootstrap equations for the out-vacuum wave function and…
We study Liouville theory on worldsheets with boundary using the solutions of Knizhnik-Zamolodchikov equation involving a degenerate representation of the Virasoro algebra. The expression for bulk-boundary propagator on a disc is proposed.
We examine periodic solutions to an initial boundary value problem for a Liouville equation with sign-changing weight. A representation formula is derived both for singular and nonsingular boundary data, including data arising from…
We prove a Liouville type classification theorem in half-spaces for infinite boundary value problems related to fully nonlinear, uniformly elliptic operators. We then apply the result in order to obtain gradient boundary blow up rates for…
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…
We study N=1 super Liouville theory on worldsheets with and without boundary. Some basic correlation functions on a sphere or a disc are obtained using the properties of degenerate representations of superconformal algebra. Boundary states…