Related papers: Coadjoint Orbits and Conformal Field Theory
We present recent progress in theory of local conformal nets which is an operator algebraic approach to study chiral conformal field theory. We emphasize representation theoretic aspects and relations to theory of vertex operator algebras…
In this work we describe the mathematical foundations used in the construction of primary fields of minimal models of conformal field theory. The work contains two parts: In the first part we give a description of Verma and Fock modules for…
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…
This article develops new techniques for understanding the relationship between the three different mathematical formulations of two-dimensional chiral conformal field theory: conformal nets (axiomatizing local observables), vertex operator…
A new rigorous approach to conformal field theory is presented. The basic objects are families of complex-valued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of…
Conformal algebra is an axiomatic description of the operator product expansion of chiral fields in conformal field theory. On the other hand, it is an adequate tool for the study of infinite-dimensional Lie algebras satisfying the locality…
We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of…
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
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…
Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. We review some main convergence results, conjectures and problems in the construction and study of…
We explore new connections between the fields and local observables in two dimensional chiral conformal field theory. We show that in a broad class of examples, the von Neumann algebras of local observables (a conformal net) can be obtained…
In this thesis we study two-dimensional conformal field theories with Virasoro algebra symmetry, following the conformal bootstrap approach. Under the assumption that degenerate fields exist, we provide an extension of the analytic…
Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal…
To certain geometries, string theory associates conformal field theories. We discuss techniques to perform the reverse procedure: To recover geometrical data from abstractly defined conformal field theories. This is done by introducing…
The main purpose of this paper is a mathematical construction of a non-perturbative deformation of a two-dimensional conformal field theory. We introduce a notion of a full vertex algebra which formulates a compact two-dimensional conformal…
In two-dimensional conformal field theory (CFT) the building blocks are given by chiral CFTs, i.e.~CFTs on the unit circle (compactified light-ray). They are generated by quantum fields depending on one light-ray coordinate only. There are…
The notion of vertex operator coalgebra is presented and motivated via the geometry of conformal field theory. Specifically, we describe the category of geometric vertex operator coalgebras, whose objects have comultiplicative structures…
It is known that there are 48 Virasoro algebras acting on the monster conformal field theory. We call conformal field theories with such a property, which are not necessarily chiral, code conformal field theories. In this paper, we…
We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories.…
Based on any chiral vertex operator algebra satisfying a suitable finiteness condition, the semisimplicity of the zero-mode algebra as well as a regularity for induced modules, we construct conformal field theory over the projective line…