Related papers: Gaussian free field and conformal field theory
These pedagogical lectures present some material, classical or more recent, on (Rational) Conformal Field Theories and their general setting ``in the bulk'' or in the presence of a boundary. Two well posed problems are the classification of…
In this paper I develop categorical foundations needed for a rigorous approach to the definition of conformal field theory outlined by Graeme Segal. I discuss pseudo algebras over theories and 2-theories, their pseudo morphisms, bilimits,…
We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian…
In this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated. These theories are realized in terms of free scalar fields starting from the simple $b-c$ systems and scalar fields on…
We consider various homotopy algebras related to Yang-Mills theory and two-dimensional conformal field theory (CFT). Our main objects of study are Yang-Mills $L_{\infty}$ and $C_{\infty}$ algebras and their relation to the certain algebraic…
These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of…
A general two dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed subalgebra generated by $(L_{-1}, L_{0},…
Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have an extended $W$ algebras which…
We review various aspects of two dimensional conformal field theories paying close attention to the algebraic structures that intervene. We provide a compact description regarding the appearance of a chiral algebra as the symmetry algebra…
We will show how the study of randomly triangulated surfaces merges with the study of open/closed string dualities. In particular we will discuss the Conformal Field Theory which arises in the open string sector and its implications.
Talk presented at the conference on representation theory and harmonic analysis at Saclay, the talk presented the development in conformal field theory since 1968
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.
In the framework of metric-like approach, totally symmetric arbitrary spin bosonic conformal fields propagating in flat space-time are studied. Depending on the values of conformal dimension, spin, and dimension of space-time, we classify…
An exact mapping is established between the $c\geq25$ Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian Free Field plus a logarithmic confining potential. The probability distribution of…
Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory. This is a review of recent developments in the subject.
We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of…
Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal…
In this article we prove smoothness of the correlation functions in probabilistic Liouville Conformal Field Theory. Our result is a step towards proving that the correlation functions satisfy the higher Ward identities and the higher BPZ…
SLE(kappa; rho), a generalization of chordal Schramm-L\"owner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be…
In this paper the free gauge field theories on a Riemann surface of any genus are quantized in the covariant gauge. The propagators of the gauge fields are explicitly derived and their properties are analysed in details. As an application,…