Related papers: Conformal Invariance and Percolation
This thesis is dedicated to analysing the general structure of two- and three-point correlation functions of conserved currents of arbitrary integer or half-integer spins in three- and four-dimensional (super)conformal field theory.
Connections are found between the two-component percolation problem and the conductor/insulator percolation problem. These produce relations between critical exponents, and suggest formulae connecting the conductivity exponents in different…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such…
Introduction to two dimensional conformal field theory on open and unoriented surfaces. The construction is illustrated in detail on the example of SU(2) WZW models.
Polyakov recently showed how to use conformal field theory to describe two-dimensional turbulence. Here we construct an infinite hierarchy of solutions, both for the constant enstrophy flux cascade, and the constant energy flux cascade. We…
We consider the densities of clusters, at the percolation point of a two-dimensional system, which are anchored in various ways to an edge. These quantities are calculated by use of conformal field theory and computer simulations. We find…
This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…
These are lectures presented at the Les Houches Summer School ``Topology and Geometry in Physics'', July 1998. They provide a simple introduction to non perturbative methods of field theory in 1+1 dimensions, and their application to the…
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…
We study four-point functions of critical percolation in two dimensions, and more generally of the Potts model. We propose an exact ansatz for the spectrum: an infinite, discrete and non-diagonal combination of representations of the…
We summarize the results obtained in the last few years about permutation orbifolds in two-dimensional conformal field theories, their application to string theory and their use in the construction of four-dimensional heterotic string…
Survival and percolation probabilities are most important quantities in the theory and in the application of growth models with spreading. We construct field theoretical expressions for these probabilities which are feasible for…
The directed bond percolation is a paradigmatic model in nonequilibrium statistical physics. It captures essential physical information on the nature of continuous phase transition between active and absorbing states. In this paper, we…
We obtain exact results for correlation functions of primary operators in the two-dimensional conformal field theory of a scalar field interacting with a critical periodic boundary potential. Amplitudes involving arbitrary bulk discrete…
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…
I review recent results on conformal field theories in four dimensions and quantum field theories interpolating between conformal fixed points, supersymmetric and non-supersymmetric. The talk is structured in three parts: i) central…
The main result of this paper is the construction of a conformally covariant operator in two dimensions acting on scalar fields and containing fourth order derivatives. In this way it is possible to derive a class of Lagrangians invariant…
An effective non-local quantum field theory is constructed, which describes interaction of pomerons in the high-coloured QCD. The theory includes both splitting and merging triple pomeron vertexes and diagrams with pomeronic loops. The…
This is a brief introduction to the subject of Conformal Field Theory on surfaces with boundaries and crosscaps, which describes the perturbative expansion of open string theory.