Related papers: Vertex Operator Superalgebras and Their Representa…
We classify the self-dual (or holomorphic) vertex operator superalgebras of central charge 24, or in physics parlance the purely left-moving, fermionic 2-dimensional conformal field theories with just one primary field. There are exactly…
It is proved that any vertex operator algebra for which the image of the Virasoro element in Zhu's algebra is algebraic over complex numbers is finitely generated. In particular, any vertex operator algebra with a finite dimensional Zhu's…
The dimension of any module over an algebra of affiliated operators ${\mathcal U}$ of a finite von Neumann algebra ${\mathcal A}$ is defined using a trace on ${\mathcal A}.$ All zero-dimensional ${\mathcal U}$-modules constitute the torsion…
We construct a factorization algebra, via the factorization envelope, starting from a Lie conformal algebra, and prove that the associated vertex algebra is isomorphic to its enveloping vertex algebra. Our construction generalizes the…
In this paper, we study representations of the vertex operator algebra $L(k,0)$ at one-third admissible levels $k= -5/3, -4/3, -2/3$ for the affine algebra of type $G_2^{(1)}$. We first determine singular vectors and then obtain a…
In this paper, we give a construction of simple modules generalizing and including both highest weight and Whittaker modules for the Neveu-Schwarz algebra, in the spirit of the work of Mazorchuk and Zhao on simple Virasoro modules. We…
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…
We give an algebraic proof of the unitarity of the vertex operator algebra $L(21/22, 0)\oplus L(21/22, 8)$ and of all its irreducible ordinary modules, using a coset realization arising from the $3C$-algebra. Motivated by the structure of…
The direct sum of irreducible level one integrable representations of affine Kac-Moody Lie algebra of (affine) type $ADE$ carries a structure of $P/Q$-graded vertex operator algebra. There exists a filtration on this direct sum studied by…
We give an abstract construction, based on the Belavin-Polyakov-Zamolodchikov equations, of a family of vertex operator algebras of rank $26$ associated to the modified regular representations of the Virasoro algebra. The vertex operators…
In this paper, we study the representation theory for the affine Lie algebra $\H$ associated to the Nappi-Witten model $H_{4}$. We classify all the irreducible highest weight modules of $\H$. Furthermore, we give a necessary and sufficient…
We propose a correspondence between vertex operator superalgebras and families of sigma models in which the two structures are related by symmetry properties and a certain reflection procedure. The existence of such a correspondence is…
We study a simple, self-dual, rational, and $C_2$-cofinite vertex operator algebra of CFT-type whose simple current modules are graded by $\mathbb{Z}_{2k}$. Based on those simple current modules, a vertex operator algebra associated with a…
We apply the factorization and vector bundle propositionerty of the sheaves of conformal blocks on $\overline{\mathscr{M}}_{g,n}$. defined by vertex operator algebras (VOAs) and give geometric proofs of essential results in the…
We investigate vertex operator algebras $L(k,0)$ associated with modular-invariant representations for an affine Lie algebra $A_1 ^{(1)}$ , where k is 'admissible' rational number. We show that VOA $L(k,0)$ is rational in the category $\cal…
For a vertex operator algebra V, a V-module M and a nonnegative integer n, an A_n(V)-bimodule A_n(M) is constructed and studied. The connection between A_n(M) and intertwining operators are discussed. In the case that V is rational, A_n(M)…
We study the general structure of Fermi conformal nets of von Neumann algebras on the circle, consider a class of topological representations, the general representations, that we characterize as Neveu-Schwarz or Ramond representations, in…
In this note we prove that the vertex operator superalgebras associated to the unitary representations of the N=2 superconformal algebra are rational.
In this paper, we investigate the theory of $g$-twisted modules for modular $\frac{1}{2}\mathbb{Z}$-graded vertex superalgebras over an algebraically closed field $\mathbb{F}$ of prime characteristic $p>2$. For a…
In the first part of my talk I will explain a solution to the extension of Lie's problem on classification of "local continuous transformation groups of a finite-dimensional manifold" to the case of supermanifolds. (More precisely, the…