相关论文: Gaussian free field and conformal field theory
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
This is an elementary review of our recent work on the classification of the spectra of those two-dimensional rational conformal field theories (RCFTs) whose (maximal) chiral algebras are current algebras. We classified all possible…
In a short review of recent work, we discuss the general problem of constructing the actions of new conformal field theories from old conformal field theories. Such a construction follows when the old conformal field theory admits new…
This monograph is dedicated to a generalization of the L\"owner equation in its stochastic form known as SLE and to its coupling with the Gaussian free field, ultimately aiming at the construction of a boundary conformal field theory with…
Over the past twenty years, the probabilistic approach to Liouville Conformal Field Theory (LCFT) has undergone remarkable developments, transforming a collection of ideas at the interface of probability, geometry, complex analysis and…
Formal Loewner evolution is connected to conformal field theory. In this letter we introduce an extension of Loewner evolution, which consists of two coupled equations and connect the martingales of these equations to the null vectors of…
This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with a pure Virasoro example, critical percolation, then continues with a detailed exposition of symplectic fermions,…
We examine general aspects of parity functions arising in rational conformal field theories, as a result of Galois theoretic properties of modular transformations. We focus more specifically on parity functions associated with affine Lie…
The aim of these notes is threefold. First, we discuss geometrical aspects of conformal covariance in stochastic Schramm-Loewner evolutions (SLEs). This leads us to introduce new ``dipolar'' SLEs, besides the known chordal, radial or…
Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.
Free Lagrangians are found both for gauge and non-gauge bosonic conformal fields of any symmetry type and in any space-time dimension. Conformal gauge fields of various types, their gauge transformations and gauge invariant field strengths…
Linear free field theories are one of the few Quantum Field Theories that are exactly soluble. There are, however, (at least) two very different languages to describe them, Fock space methods and the Schroedinger functional description. In…
It is discussed how stochastic evolutions may be linked to logarithmic conformal field theory. This introduces an extension of the stochastic Loewner evolutions. Based on the existence of a logarithmic null vector in an indecomposable…
The ADE classification scheme is encountered in many areas of mathematics, most notably in the study of Lie algebras. Here such a scheme is shown to describe families of two-dimensional conformal field theories.
This primer is an introduction to Conformal Field Theory in $D\geq3$. It is designed to introduce the reader to many of the important foundational concepts and methods in CFT. In it, pig picture ideas are prioritized over technical details,…
Parafermionic conformal field theories are considered on a purely algebraic basis. The generalized Jacobi type identity is presented. Systems of free fermions coupled to each other by nontrivial parafermionic type relations are studied in…
We develop a version of dipolar conformal field theory based on the central charge modification of the Gaussian free field with the Dirichlet boundary condition and prove that correlators of certain family of fields in this theory are…
Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical…
The lectures provide a pedagogical introduction to the methods of CFT as applied to two-dimensional critical behaviour.
This is a writeup of lectures given at the EPFL Lausanne in the fall of 2012. The topics covered: physical foundations of conformal symmetry, conformal kinematics, radial quantization and the OPE, and a very basic introduction to conformal…