Related papers: Logarithmic Conformal Null Vectors and SLE
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
In statistical mechanics, observables are usually related to local degrees of freedom such as the Q < 4 distinct states of the Q-state Potts models or the heights of the restricted solid-on-solid models. In the continuum scaling limit,…
We review recent work in machine learning aspects of conformal field theory and Lie algebra representation theory using neural networks.
We construct Euclidean Liouville conformal field theories in odd number of dimensions. The theories are nonlocal and non-unitary with a log-correlated Liouville field, a ${\cal Q}$-curvature background, and an exponential Liouville-type…
We propose a generalization of Schramm-Loewner evolution (SLE) that has internal degrees of freedom described by an affine Lie superalgebra. We give a general formulation of SLE corresponding to representation theory of an affine Lie…
The relativistic formulation of abstract evolution equations is introduced. The corresponding logarithmic representation is shown to exist without assuming the invertible property of evolution operators. Consequently, by means of the…
We discuss the problem to develop a mathematical theory of a certain class of nonrational conformal field theories (CFT) which contain the unitary CFT. A variant of the concept of a modular functor is proposed that appears to be suitable…
Logarithmic Conformal Field Theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self avoiding walks, etc.), or of critical points in several classes of disordered systems…
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 present basic properties of Dipolar SLEs, a new version of stochastic Loewner evolutions (SLE) in which the critical interfaces end randomly on an interval of the boundary of a planar domain. We present a general argument explaining why…
We present remarkable properties of the groups SL2(Z/NZ) which might be useful in detailed studies of some quotients appearing in Conformal Field Theories.
In this note, some aspects of the generalization of a primary field to the logarithmic scenario are discussed. This involves understanding how to build Jordan blocks into the geometric definition of a primary field of a conformal field…
It is discussed how a limiting procedure of (super)conformal field theories may result in logarithmic (super)conformal field theories. The construction is illustrated by logarithmic limits of (unitary) minimal models in conformal field…
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.
The smallest deformation of the minimal model M(2,3) that can accommodate Cardy's derivation of the percolation crossing probability is presented. It is shown that this leads to a consistent logarithmic conformal field theory at c=0. A…
We consider the conformal properties of geometries described by higher-rank line elements. A crucial role is played by the conformal Killing equation (CKE). We introduce the concept of null-flat spaces in which the line element can be…
We study the conformal classes of 2-dimensional Lorentzian tori with (non zero) Killing fields. We define a map that associate to such a class a vector field on the circle (up to a scalar factor). This map is not injective but has finite…
Conformal algebra is an axiomatic description of the operator product expansion of chiral fields in conformal field theory. On the other hand, it is an adequate tool for the study of infinite-dimensional Lie algebras satisfying the locality…
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.
We define Lie algebroids over infinite jet spaces and establish their equivalent representation through homological evolutionary vector fields.