Related papers: Probabilistic interpretation of quantum field theo…
This is an introduction to the microscopic techniques of non-rational bulk and boundary conformal field theory which are needed to describe strings moving in non-compact curved backgrounds. The latter arise e.g. in the context of…
Following the 1984 seminal work of Belavin, Polyakov and Zamolodchikov on two-dimensional conformal field theories, Toda conformal field theories were introduced in the physics literature as a family of two-dimensional conformal field…
Liouville field theory has long been a cornerstone of two-dimensional quantum field theory and quantum gravity, which has attracted much recent attention in the mathematics literature. Timelike Liouville field theory is a version of…
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…
The conjecture about the correspondence between instanton partition functions in the N=2 SUSY Yang-Mills theory and conformal blocks of two-dimensional conformal field theories is extended to the case of the N=1 supersymmetric conformal…
A new conformal field theory description of two-dimensional turbulence is proposed. The recently established class of rational logarithmic conformal field theories provides a unique candidate solution which resolves many of the drawbacks of…
We explain the basics of conformal theory using the language of chiral algebras of Beilinson and Drinfeld.
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
We review recent work in machine learning aspects of conformal field theory and Lie algebra representation theory using neural networks.
In this work we construct Liouville quantum gravity on an annulus in the complex plane. This construction is aimed at providing a rigorous mathematical framework to the work of theoretical physicists initiated by Polyakov in 1981. It is…
In this article a non--technical survey is given of the present status of Axiomatic Quantum Field Theory and interesting future directions of this approach are outlined. The topics covered are the universal structure of the local algebras…
We study four-point correlation functions with logarithmic behaviour in Liouville field theory on a sphere, which consist of one kind of the local operators. We study them as non-integrated correlation functions of the gravitational sector…
In a recent paper (arXiv:0906.3219) the representation of Nekrasov partition function in terms of nontrivial two-dimensional conformal field theory has been suggested. For non-vanishing value of the deformation parameter…
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…
Quantization of two-dimensional dilaton gravity coupled to conformal matter is investigated. Working in conformal gauge about a fixed background metric, the theory may be viewed as a sigma model whose target space is parameterized by the…
We develop a perturbative expansion of quantum Liouville theory on the pseudosphere around the background generated by heavy charges. Explicit results are presented for the one and two point functions corresponding to the summation of…
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…
I explain the motivation for investigating the high energy limit of QCD and give a brief presentation of recent progress in the understanding of unitarity corrections in this kinematic regime. Special emphasis is given to the conformal…
A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Applying the generators of the closed subalgebra generated by…
Toda Conformal Field Theories (CFTs hereafter) are generalizations of Liouville CFT where the underlying field is no longer scalar but takes values in a finite-dimensional vector space induced by a complex simple Lie algebra. The goal of…