Geometric interpretation of vertex operator algebras.
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Vafa's approach to the formulation of conformal field theories is combined with the formal calculus developed in Frenkel, Lepowsky, and Meurman's work on the vertex operator construction of the Monster to give a geometric definition of vertex operator algebras.Abstract:
In this paper, Vafa's approach to the formulation of conformal field theories is combined with the formal calculus developed in Frenkel, Lepowsky, and Meurman's work on the vertex operator construction of the Monster to give a geometric definition of vertex operator algebras. The main result announced is the equivalence between this definition and the algebraic one in the sense that the categories determined by these definitions are isomorphic.read more
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Journal ArticleDOI
Modular invariance of characters of vertex operator algebras
TL;DR: In this article, it was shown that the characters of the integrable highest weight modules of affine Lie algebras and the minimal series of the Virasoro algebra give rise to conformal field theories.
Journal ArticleDOI
Local systems of vertex operators, vertex superalgebras and modules
TL;DR: In this article, it was shown that the vertex operator superalgebra V has a vertex (super)algebra structure with M as a module, and for a vertex operator V, giving a V-module M is equivalent to giving a vertex operators homomorphism from V to some local system of vertex operators on a vector space.
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Local Systems of Vertex Operators, Vertex Superalgebras and Modules
TL;DR: The notion of vertex operator superalgebras was introduced in this paper, where it was shown that any local system of vertex operators on a super vector space has a natural vertex (super)algebra structure with $M$ as a module.
Journal ArticleDOI
A theory of tensor products for module categories for a vertex operator algebra, III
Yi-Zhi Huang,James Lepowsky +1 more
TL;DR: In this article, a tensor product theory for modules for a vertex operator algebra is developed, where the goal is to construct a "vertex tensor category" structure on the category of modules.
Book ChapterDOI
Tensor Products of Modules for a Vertex Operator Algebra and Vertex Tensor Categories
Yi-Zhi Huang,James Lepowsky +1 more
TL;DR: In this article, a tensor product theory of classes of modules for vertex operator algebra is presented, which is based on both the formal-calculus approach to vertex algebra theory developed in [FLM2] and [FHL] and the precise geometric interpretation of the notion of vertex algebra established in [H1].