Related papers: EPFL Lectures on Conformal Field Theory in D>= 3 D…
The following are expanded lecture notes for the course of eight one hour lectures given by the second author at the 2014 summer school Asymptotic Analysis in General Relativity held in Grenoble by the Institut Fourier. The first four…
I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3) solutions to the WDVV equations of topological…
We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic…
In this thesis we study two-dimensional conformal field theories with Virasoro algebra symmetry, following the conformal bootstrap approach. Under the assumption that degenerate fields exist, we provide an extension of the analytic…
We consider logarithmic conformal field theories near a boundary and derive the general form of one and two point functions. We obtain results for arbitrary and two dimensions. Application to two dimensional magnetohydrodynamics is…
We give an introduction to the structure theory of extended affine Lie algebras, which provide a common framework for finite-dimensional semisimple, affine and toroidal Lie algebras. The notes are based on a lecture series given during the…
Light-cone formulation of conformal field theory in space-time of arbitrary dimension is developed. Conformal fundamental and shadow fields with arbitrary conformal dimension and arbitrary spin are studied. Representation of conformal…
A simple realization of the conformal higher spin symmetry on the free $3d$ massless matter fields is given in terms of an auxiliary Fock module both in the flat and $AdS_3$ case. The duality between non-unitary field-theoretical…
We consider a conformal field theory in two dimensions in which an external perturbation is placed. We study the energy flux and entanglement entropy for one, two and multiple intervals and give a suggestion relating the two in some cases.…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
We present a conformal theory of a dissipationless relativistic fluid in 2 space-time dimensions. The theory carries with it a representation of the algebra of 2-$D$ area-preserving diffeomorphisms in the target space of the complex scalar…
We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…
(Revised LaTex version).The structure of free field representation and some correlation functions of the SU(3) CFT are considered.
Several aspects of fusion rings and fusion rule algebras, and of their manifestations in twodimensional (conformal) field theory, are described: diagonalization and the connection with modular invariance; the presentation in terms of…
We give an introduction to conformal and superconformal algebras and their representations in various dimensions. Special emphasis is put on 4d $\mathcal{N}=2$ superconformal symmetry. This is the writeup of the lectures given at the Winter…
This is a write-up of some lectures I gave in the Fall of 2021 at the Fields Institute in Toronto, as part of the Thematic Programme on Trends in Pure and Applied Model Theory. The goal of the module was to give a quick introduction to the…
We outline a relationship between conformal field theories and spectral problems of ordinary differential equations, and discuss its generalisation to models related to classical Lie algebras.
This paper is based on my presentation at RIMS workshop on "Theory of Integrable Systems and Its Applications in Various Fields" held in Kyoto on 19--21, August 2015. The aim of the present paper is to give a short account of recent studies…
From conformal field theory on the Riemann sphere, we implement its boundary version in a simply-connected domain using the Schottky double construction. We consider the statistical fields generated by background charge modification of the…
We describe conformal field theories, correlation functions of which satisfy equations of the two-dimensional fluid mechanics. Prediction for the energy spectrum is given, $E(k) \sim k^{-25/7}$.