Related papers: Classical conformal blocks, Coulomb gas integrals,…

We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field…

It is shown that, under the Wentzel-Kramers-Brillouin approximation conditions, using the Foldy-Wouthuysen representation allows the problem of finding a classical limit of relativistic quantum mechanical equations to be reduced to the…

In these proceedings we review the results of [1-3]. We show on the example of the SU(2) chiral-field how to reproduce the classical finite gap solutions for a large class of integrable sigma models from their exact quantum solutions. These…

We will describe how logarithmic singularities arise as limits of Coulomb Gas integrals. Our approach will combine analytic properties of the time-like Liouville structure constants, together with the recursive formula of the Virasoro…

A challenge in the study of conformal field theory (CFT) is to characterize the possible defects in specific bulk CFTs. Given the success of numerical bootstrap techniques applied to the characterization of bulk CFTs, it is desirable to…

Conformal blocks for correlation functions of tensor operators play an increasingly important role for the conformal bootstrap programme. We develop a universal approach to such spinning blocks through the harmonic analysis of certain…

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…

A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level $k$. In contrast to the more familiar…

Bootstrap equations for conformal correlators that mimic the early theory of conformal bootstrap are written down in frames of the AdS/CFT approach. The simplified version of these equations, that may be justified if Schwinger-Keldysh…

Considering two dimensional gravity coupled to a CFT, we show that a semiclassical black hole can be described in terms of two Liouville theories matched at the horizon. The black hole exterior corresponds to a space-like while the interior…

Defects which are predominant in a realistic model, usually spoil its integrability or solvability. We on the other hand show the exact integrability of a known sine-Gordon field model with a defect (DSG), at the classical as well as at the…

Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the…

Warped conformal field theory (WCFT) is a two dimensional quantum field theory whose local symmetry algebra consists of a Virasoro algebra and a U(1) Kac-Moody algebra. In this paper, we study correlation functions for primary operators in…

We propose a systematic method to extract conformal loop models for rational conformal field theories (CFT). Method is based on defining an ADE model for boundary primary operators by using the fusion matrices of these operators as…

We study scalar conformal field theories whose large $N$ spectrum is fixed by the operator dimensions of either Ising model or Lee-Yang edge singularity. Using numerical bootstrap to study CFTs with $S_N\otimes Z_2$ symmetry, we find a…

We introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to operators with spin. The key idea is to implement the…

The primary aim of these lecture notes is to introduce the modern approach to two-dimensional conformal field theory (2D CFT). The study of analytical methods in two-dimensional conformal field theory has developed over several decades,…

This is a set of introductory lecture notes on conformal field theory. Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. It begins with a…

A quantum-field model of the conformally flat space is formulated using a standard field-theoretical technique, a probability interpretation and a way to establish the classical limit. The starting point is the following: after conformal…

The construction of conformal blocks for the analysis of multipoint correlation functions with $N > 4$ local field insertions is an important open problem in higher dimensional conformal field theory. This is the first in a series of papers…