Related papers: Classification of operator algebraic conformal fie…
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…
The conformal anomaly and the Virasoro algebra are fundamental aspects of 2D conformal field theory and conformally covariant models in planar random geometry. In this article, we explicitly derive the Virasoro algebra from an…
Let $L(-{1/2}(l+1),0)$ be the simple vertex operator algebra associated to an affine Lie algebra of type $A_{l}^{(1)}$ with the lowest admissible half-integer level $-{1/2}(l+1)$, for even l. We study the category of weak modules for that…
We introduce a new class of two dimensional conformal field theories by extending Wess-Zumino-Witten (WZW) models to chiral algebras with matrix-valued levels. The new CFTs are based on holomorphic currents with an operator product…
We describe an approach to classifying four-dimensional conformal field theories with N=2 supersymmetry and a Coulomb branch of vacua with the topology of the complex plane. We also discuss the Higgs/mixed branches and conformal/flavor…
This paper presents a unified algebraic, topological, and logical framework for electrical one-port networks based on \v{S}are's $m$-theory. Within this formalism, networks are represented by $m$-words (jorbs) over an ordered alphabet,…
We present a classification of $W$ algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with an $Sl(2)$ subalgebra (resp. $OSp(1|2)$ superalgebra)…
We show that every unitary positive energy representation W of the Virasoro algebra exponentiates to a holomorphic *-representation of the semigroup of annuli by bounded operators on the Hilbert space completion of W. We use this to show…
The affine vertex operator algebras for $\mathfrak{sl}_2$ and the Virasoro minimal models are related by Drinfeld-Sokolov reduction and by the Goddard-Kent-Olive coset construction. In this work, we propose another connection based on…
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…
A graded generalization of the Z_k parafermionic current osp(1|2)/U(1) coset conformal field theory. The structure of the parafermionic highest-weight modules is analyzed and the dimensions of the fields of the theory are determined. A free…
A list of superconformal chiral operator product expansion algebras with quadratic nonlinearity in two dimensions is completed on the basis of the known classification of little conformal Lie superalgebras. In addition to the previously…
In this talk, I will review the foundations of irrational conformal field theory (ICFT), which includes rational conformal field theory as a small subspace. Highlights of the review include the Virasoro master equation, the Ward identities…
These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in…
The classification of CFTs has an important subproblem, namely classifiying the partition functions for WZW theories. This subproblem is intimately connected to the modular behaviour of the characters of affine algebras. This paper…
We describe a general way of constructing integrable defect theories as perturbations of conformal field theory by local defect operators. The method relies on folding the system onto a boundary field theory of twice the central charge. The…
In this thesis we develop an orbifold theory for a finite, cyclic group $G$ acting on a suitably regular, holomorphic vertex operator algebra $V$. To this end we describe the fusion algebra of the fixed-point vertex operator subalgebra…
We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted $\R\times \R$-graded full field algebra is equivalent to an algebra over a partial operad constructed…
Representations of vertex operator algebras define sheaves of coinvariants and conformal blocks on moduli of stable pointed curves. Assuming certain finiteness and semisimplicity conditions, we prove that such sheaves satisfy the…
We study connections between closure operators on an algebra $(A,\Om)$ and congruences on the extended power algebra defined on the same algebra. We use these connections to give an alternative description of the lattice of all subvarieties…