相关论文: Geometric realization of algebraic conformal field…
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…
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…
We formulate conformal field theory in the setting of algebraic quantum field theory as Haag-Kastler nets of local observable algebras with diffeomorphism covariance on the two-dimensional Minkowski space. We then obtain a decomposition of…
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…
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 is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We review the following algebraic structures which appear in two-dimensional conformal field theory (CFT): The symmetries of two-dimensional…
Unitary vertex operator algebras (VOAs) and conformal nets are the two most prominent mathematical axiomatizations of two-dimensional unitary chiral conformal field theories. They are conjectured to be equivalent, but a rigorous comparison…
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…
We comment on a program designed for the study of local chiral algebras and their representations in 2D conformal field theory. Based on the algebraic approach described by W. Nahm, this program efficiently calculates arbitrary n-point…
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…
The connection between Riemann surfaces with boundaries and the theory of vertex operator algebras is discussed in the framework of conformal field theories defined by Kontsevich and Segal and in the framework of their generalizations in…
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…
In the presence of an $\Omega$-deformation, local operators generate a chiral algebra in the topological-holomorphic twist of a four-dimensional $\mathcal{N} = 2$ supersymmetric field theory. We show that for a unitary $\mathcal{N} = 2$…
We provide an Operator Algebraic approach to N=2 chiral Conformal Field Theory and set up the Noncommutative Geometric framework. Compared to the N=1 case, the structure here is much richer. There are naturally associated nets of spectral…
C denotes either the conformal group in 3+1 dimensions, or in one chiral dimension. Let U be a unitary, strongly continuous representation of C satisfying the spectrum condition and inducing, by its adjoint action, automorphisms of a…
This thesis describes a new approach to conformal field theory. This approach combines the method of coadjoint orbits with resolutions and chiral vertex operators to give a construction of the correlation functions of conformal field…
We describe a coordinate-free notion of conformal nets as a mathematical model of conformal field theory. We define defects between conformal nets and introduce composition of defects, thereby providing a notion of morphism between…
We prove an equivalence between the following notions: (i) unitary M\"obius vertex algebras, and (ii) Wightman conformal field theories on the circle (with finite-dimensional conformal weight spaces) satisfying an additional condition that…
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 discuss some open problems in a program of constructing and studying two-dimensional conformal field theories using the representation theory of vertex operator algebras.