Related papers: Conformal Field Theory, Tensor Categories and Oper…
For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
We formulate the unitary rational orbifold conformal field theories in the algebraic quantum field theory framework. Under general conditions, we show that the orbifold of a given unitary rational conformal field theories generates a…
This is the first part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. This theory generalizes the tensor category theory for…
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…
A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Applying the generators of the closed subalgebra generated by…
The main properties of indefinite Kac-Moody and Borcherds algebras, considered in a unified way as Lorentzian algebras, are reviewed. The connection with the conformal field theory of the vertex operator construction is discussed. By the…
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 explain the basics of conformal theory using the language of chiral algebras of Beilinson and Drinfeld.
We present a comprehensive method for the evaluation of a vast class of integrals representing 3-point functions of conformal field theories in momentum space. The method leads to analytic, closed-form expressions for all scalar and…
We solve the problem of constructing a genus-zero full conformal field theory (a conformal field theory on genus-zero Riemann surfaces containing both chiral and antichiral parts) from representations of a simple vertex operator algebra…
We consider logarithmic conformal field theories near a boundary and derive the general form of one and two point functions. We obtain results for arbitrary and two dimensions. Application to two dimensional magnetohydrodynamics is…
It is shown explicitly that the correlation functions of Conformal Field Theories (CFT) with the logarithmic operators are invariant under the differential realization of Borel subalgebra of $\W_\infty$-algebra. This algebra is constructed…
These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students,…
Conformal field theory and its axiomatisation in terms of vertex operator algebras or chiral algebras are most commonly considered on the Riemann sphere. However, an important constraint in physics and an interesting source of mathematics…
This is an introduction to two-dimensional conformal field theory and its applications in string theory. Modern concepts of conformal field theory are explained, and it is outlined how they are used in recent studies of D-branes in the…
Rational chiral conformal field theories are organized according to their genus, which consists of a modular tensor category $\mathcal{C}$ and a central charge $c$. A long-term goal is to classify unitary rational conformal field theories…
These lecture notes provide a comprehensive introduction to 2d conformal field theory, covering foundational topics such as free fields, minimal models, Zamolodchikov's $c$-theorem, Wess-Zumino-Witten models, modular invariant partition…
The lectures provide a pedagogical introduction to the methods of CFT as applied to two-dimensional critical behaviour.
This is a set of introductory lecture notes devoted to the Wess-Zumino-Witten model of two-dimensional conformal field theory. We review the construction of the exact solution of the model from the functional integral point of view. The…