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Vertex operator algebras: Finite-dimensional cases and conformal blocks

Show simple item record Andrews, George 2022-05-11T10:51:04Z 2022-05-11T10:51:04Z 2022-04-29
dc.description.abstract Vertex operator algebras are algebraic objects analogous to both commutative associative algebras with identity and Lie algebras. They provide a way of rigorously constructing a particular family of quantum field theories called rational conformal field theories. In this thesis we construct the simplest class of examples of vertex operator algebras, namely the finite dimensional ones, and prove basic results on modules of these vertex operator algebras and spaces of conformal blocks associated to smooth projective curves. We also construct the vertex operator algebra associated with the $\mathfrak{sl}_2(\mathbb{C})$ WZW model in the non-critical case. When combined with the FRS theorem for rational conformal field theories, vertex operator algebra theory can be used to rigorously construct one of the simplest examples of holographic duality: the Chern-Simons-WZW model correspondence. en_US
dc.rights Attribution-NonCommercial-NoDerivs 3.0 United States *
dc.rights.uri *
dc.subject vertex operator algebra en_US
dc.subject conformal block en_US
dc.title Vertex operator algebras: Finite-dimensional cases and conformal blocks en_US
dc.type Thesis en_US

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