Related papers: Limits of Vertex Algebras and Large N Factorizatio…
Factorization algebras are local-to-global objects living on manifolds, and they arise naturally in mathematics and physics. Their local structure encompasses examples like associative algebras and vertex algebras; in these examples, their…
A superfield formalism for quantum fields with N-extended superconformal symmetry is developed using vertex algebra techniques in four dimensions.
Vertex algebras that arise from four-dimensional, $\mathcal{N}=2$ superconformal field theories inherit a collection of novel structural properties from their four-dimensional ancestors. Crucially, when the parent SCFT is unitary, the…
We introduce and study the notion of a logarithmic vertex algebra, which is a vertex algebra with logarithmic singularities in the operator product expansion of quantum fields; thus providing a rigorous formulation of the algebraic…
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 study the moduli space of four dimensional ordinary Lie algebras, and their versal deformations. Their classification is well known; our focus in this paper is on the deformations, which yield a picture of how the moduli space is…
We show that the vortex moduli space in non-abelian supersymmetric N=(2,2) gauge theories on the two dimensional plane with adjoint and anti-fundamental matter can be described as an holomorphic submanifold of the instanton moduli space in…
We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer…
We find sufficient conditions for the construction of vertex algebraic intertwining operators, among generalized Verma modules for an affine Lie algebra $\hat{\mathfrak{g}}$, from $\mathfrak{g}$-module homomorphisms. When…
In this exposition, I discuss several developments in the theory of vertex operator algebras, and I include motivation for the definition.
We develop vertex and factorisation algebra analogues of the theory of quasitriangular bialgebras. Analogously to the classical theory, we prove their categories of representations are controlled by spectral R-matrices. In the vertex…
In this paper, we study the construction of the supersymmetric extensions of vertex algebras. In particular, for $N = n \in \mathbb{Z}_{+}$, we show the universal enveloping $N = n$ supersymmetric (SUSY) vertex algebra of an $N = n$ SUSY…
This is a paper in a series systematically to study toroidal vertex algebras. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In…
In recent work, Wang and the third author defined a class of 'extremal' vertex operator algebras (VOAs), consisting of those with at least two simple modules and conformal dimensions as large as possible for the central charge. In this…
Spanning sets for vertex operator algebras satisfying difference-zero and difference-one conditions have been extensively studied in the recent years. In this paper, we extend these results. More specifically, we show that for a suitably…
We overview classifications of simple infinite-dimensional complex $\mathbb{Z}$-graded Lie (super)algebras of polynomial growth, and their deformations. A subset of such Lie (super)algebras consist of vectorial Lie (super)algebras whose…
We introduce the notion of a genus and its mass for vertex algebras. For lattice vertex algebras, their genera are the same as those of lattices, which plays an important role in the classification of lattices. We derive a formula relating…
We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.
Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus…
This book offers an introduction to vertex algebra based on a new approach. The new approach says that a vertex algebra is an associative algebra such that the underlying Lie algebra is a vertex Lie algebra. In particular, vertex algebras…