Related papers: From vertex operator algebras to conformal nets an…

We generalize the Carpi-Kawahigashi-Longo-Weiner correspondence between vertex operator algebras and conformal nets to the case of vertex operator superalgebras and graded-local conformal nets by introducing the notion of strongly…

Herein we study conformal vectors of a Z-graded vertex algebra of (strong) CFT type. We prove that the full vertex algebra automorphism group transitively acts on the set of the conformal vectors of strong CFT type if the vertex algebra is…

We apply an idea of framed vertex operator algebras to a construction of local conformal nets of (injective type III_1) factors on the circle corresponding to various lattice vertex operator algebras and their twisted orbifolds. In…

Let $V$ be one of the following unitary strongly-rational VOAs: unitary WZW models, discrete series W-algebras of type ADE, even lattice VOAs, parafermion VOAs, their tensor products, and their strongly-rational cosets. Let $U$ be a…

We show the strong graded locality of all unitary minimal W-algebras, so that they give rise to irreducible graded-local conformal nets. Among these unitary vertex superalgebras, up to taking tensor products with free fermion vertex…

In the references [HL1]--[HL5] and [H1], a theory of tensor products of modules for a vertex operator algebra is being developed. To use this theory, one first has to verify that the vertex operator algebra satisfies certain conditions. We…

We give an analogue for vertex operator algebras and superalgebras of the notion of endomorphism ring of a vector space by means of a notion of ``local system of vertex operators'' for a (super) vector space. We first prove that any local…

This is a continuation of our work to understand vertex operator algebras using the geometric properties of varieties attached to vertex operator algebras. For a class of vertex operator algebras including affine vertex operator algebras…

In this article, we show that a framed vertex operator algebra V satisfying the conditions: (1) V is holomorphic (i.e., V is the only irreducible V-module); (2) V is of rank 24; and (3) V_1=0; is isomorphic to the moonshine vertex operator…

On a conformal net $\mathcal{A}$, one can consider collections of unital completely positive maps on each local algebra $\mathcal{A}(I)$, subject to natural compatibility, vacuum preserving and conformal covariance conditions. We call…

This paper is the first in a series of papers developing a functional-analytic theory of vertex (operator) algebras and their representations. For an arbitrary Z-graded finitely-generated vertex algebra (V, Y, 1) satisfying the standard…

This paper is a continuation to understand Heisenberg vertex algebras in terms of moduli spaces of their conformal structures. We study the moduli space of the conformal structures on a Heisenberg vertex algebra that have the standard fixed…

We introduce the notion of ``local system of $\Bbb{Z}_{T}$-twisted vertex operators'' on a $\Bbb{Z}_{2}$-graded vector space $M$, generalizing the notion of local system of vertex operators [Li]. First, we prove that any local system of…

Let $V\subseteq A$ be a conformal inclusion of vertex operator algebras and let $\mathcal{C}$ be a category of grading-restricted generalized $V$-modules that admits the vertex algebraic braided tensor category structure of…

A regular vertex operator algebra is a vertex operator algebra such that any weak module (without grading) is a direct sum of ordinary irreducible modules. In this paper we give several sufficient conditions under which a rational vertex…

Let V be a simple unitary vertex operator algebra and U be a (polynomially) energy-bounded unitary subalgebra containing the conformal vector of V. We give two sufficient conditions implying that V is energy-bounded. The first condition is…

We apply the general theory of tensor products of modules for a vertex operator algebra developed in our papers hep-th/9309076, hep-th/9309159, hep-th/9401119, q-alg/9505018, q-alg/9505019 and q-alg/9505020 to the case of the…

In this paper, we study a class of simple OZ-type vertex operator algebras $V$ generated by simple Virasoro vectors $\omega^{ij}=\omega^{ji}$, $1\leq i<j\leq n$, $n\geq 3$. We prove that $V$ is uniquely determined by its Griess algebra…

We prove that all nice holomorphic vertex operator superalgebras (VOSAs) with central charge at most 24 and with non-trivial odd part are unitary, apart from the hypothetical ones arising as fake copies of the shorter moonshine VOSA or of…

Suppose $V^G$ is the fixed-point vertex operator subalgebra of a compact group $G$ acting on a simple abelian intertwining algebra $V$. We show that if all irreducible $V^G$-modules contained in $V$ live in some braided tensor category of…