Related papers: Boundary Liouville Field Theory: Boundary Three Po…
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.…
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.…
Liouville field theory on an unoriented surface is investigated, in particular, the one point function on a RP^2 is calculated. The constraint of the one point function is obtained by using the crossing symmetry of the two point function.…
An explicit construction for the monodromy of the Liouville conformal blocks in terms of Racah-Wigner coefficients of the quantum group U_q(sl(2,R)) is proposed. As a consequence, crossing-symmetry for four point functions is analytically…
Liouville conformal field theory (LCFT) is considered on a simply connected domain with boundary, specializing to the case where the Liouville potential is integrated only over the boundary of the domain. We work in the probabilistic…
In this paper, exact one-point functions of N=1 super-Liouville field theory in two-dimensional space-time with appropriate boundary conditions are presented. Exact results are derived both for the theory defined on a pseudosphere with…
An analytic expression is proposed for the three-point function of the exponential fields in the Liouville field theory on a sphere. In the classical limit it coincides with what the classical Liouville theory predicts. Using this function…
We study mini-superspace semiclassical limit of the boundary three-point function in the Liouville field theory. We compute also matrix elements for the Morse potential quantum mechanics. An exact agreement between the former and the latter…
It is shown that in the two-exponential version of Liouville theory the coefficients of the three-point functions of vertex operators can be determined uniquely using the translational invariance of the path integral measure and the…
Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) on manifolds with a boundary. We can use conformal symmetry to constrain correlation functions of conformal invariant fields. We compute two-point and…
In this dissertation we present some basic features about Liouville and $\mathcal{N}=1$ Super Liouville Theory, and focus in the computation of their three point functions. Additionally, we include an introduction to Conformal Field…
Topological field theory in three dimensions provides a powerful tool to construct correlation functions and to describe boundary conditions in two-dimensional conformal field theories.
We consider a generalization of the two-dimensional Liouville conformal field theory to any number of even dimensions. The theories consist of a log-correlated scalar field with a background $\mathcal{Q}$-curvature charge and an exponential…
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…
Three-point correlation function in perturbed conformal field theory coupled to two-dimensional quantum gravity (perturbed Liouville gravity) is explicitly computed by using the free field approach. The representation considered here is 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…
We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of…
In the gravitational context, Liouville theory is the two-dimensional conformal field theory that controls the boundary dynamics of asymptotically AdS_3 spacetimes at the classical level. By taking a suitable limit of the coupling constants…
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…