Related papers: Constructive Liouville Conformal Field Theory
This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.
The aim of this note is to propose an interpretation for the full (non-chiral) correlation functions of the Liouville conformal field theory within the context of the quantization of spaces of Riemann surfaces.
The lectures provide a pedagogical introduction to the methods of CFT as applied to two-dimensional critical behaviour.
General properties of perturbed conformal field theory interacting with quantized Liouville gravity are considered in the simplest case of spherical topology. We discuss both short distance and large distance asymptotic of the partition…
A comprehensive introduction to two-dimensional conformal field theory is given.
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.…
We study the problem of analytic continuation of Liouville Conformal Field Theory using the probabilistic approach of David, Kupiainen, Rhodes and Vargas [DKRV16] based on the theory of Gaussian Multiplicative Chaos. The key idea is to…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
Liouville field theory on hyperelliptic surface is considered. The partition function of the Liouville field theory on the hyperelliptic surface are expressed as a correlation function of the Liouville vertex operators on a sphere and the…
In this work it is proposed a transformation which is useful in order to simplify non-polynomial potentials given in the form of an exponential. As an application, it is shown that the quantum Liouville field theory may be mapped into a…
This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. This review also attempts to provide a physical context in which to interpret these results by…
An overview of the accomplishments of constructive quantum field theory is provided.
Liouville conformal field theory is a prototypical example of an exactly solvable quantum field theory, in the sense that the correlation functions in an arbitrary background can be determined exactly using only the constraints of unitarity…
A comparison is made between proposals for the exact three point function in Liouville quantum field theory and the nonperturbative weak coupling expansion developed long ago by Braaten, Curtright, Ghandour, and Thorn. Exact agreement to…
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…
The Liouville field theory on Z_N-Riemann surfaces is studied and it is shown that it decomposes into a Liouville field theory on the sphere and N-1 free boson theories. Also, the partition function of the Liouville field theory on the…
V. Drinfeld proposed conjectures on geometric Langlands correspondence and its quantum deformation. We refine these conjectures and propose their relationship with algebraic conformal field theory.
In this note, we give a unified rigorous construction for the Liouville conformal field theory on compact Riemann surface with boundaries for $\gamma\in (0,2]$ and prove a certain type of Markov property. We also prove some fusion-type…
A rigorous probabilistic construction of Liouville conformal field theory (LCFT) on the Riemann sphere was recently given by David-Kupiainen and the last two authors. In this paper, we focus on the connection between LCFT and the classical…
We review both the construction of conformal blocks in quantum Liouville theory and the quantization of Teichm\"uller spaces as developed by Kashaev, Checkov and Fock. In both cases one assigns to a Riemann surface a Hilbert space acted on…