Related papers: Random loops and conformal field theory
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
We study examples where conformal invariance implies triviality of the underlying quantum field theory.
The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…
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 study examples where conformal invariance implies rational critical indices, triviality of the underlying quantum field theory and emergence of hypergeometric functions as solutions of the field equations.
In this thesis we investigate invariant transversals in finite groups by studying the connection between right conjugacy closed loops and finite groups. The interplay between loop theory and group theory has prompted discoveries in both…
We review the recently developed relation between the traditional algebraic approach to conformal field theories and the more recent probabilistic approach based on stochastic Loewner evolutions. It is based on implementing random conformal…
Non-relativistic conformal field theory describes many-body physics at unitarity. The correlation functions of the system are fixed by the requirement of conformal invariance. In this article, we discuss the correlation functions of scalar…
Effective field theories of two-dimensional lattice models of fluctuating loops are constructed by mapping them onto random surfaces whose large scale fluctuations are described by a Liouville field theory. This provides a geometrical view…
The methods of conformal field theory are used to obtain the series of exact solutions of the fundamental equations of the theory of turbulence. The basic conjecture, proved to be self-consistent ,is the conformal invariance of the inertial…
In this note we provide a gentle introduction to the concepts and intuition behind the recent breakthrough results on the mathematically rigorous construction of a non-trivial 2D conformal field theory, namely the so-called Liouville…
Recently, a new approach, based on boundary conformal field theory, has been applied to a variety of quantum impurity problems in condensed matter and particle physics. A particularly enlightening example is the multi-channel Kondo problem.…
The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…
We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps.…
We develop a coarse-graining procedure for two-dimensional models of fluctuating loops by mapping them to interface models. The result is an effective field theory for the scaling limit of loop models, which is found to be a Liouville…
Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our…
We discuss the partition function point of view for chordal Schramm-Loewner evolutions and their relationship with correlation functions in conformal field theory. Both are closely related to crossing probabilities and interfaces in…
This is a review of two-dimensional conformal field theory including some of the relations to integrable models. An effort is made to develop the basic formalism in a way which is as elementary and flexible as possible at the same time.…
A comprehensive introduction to two-dimensional conformal field theory is given.
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…