Date of Award

1-1-2020

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (v, 88 pages)

Dissertation/Thesis Chair

Antun Milas

Committee Members

Michael Penn, Cristian Lenart, Alexandre Tchernev

Keywords

Vertex Algebra, W-Algebras, Vertex operator algebras, Orbifolds, Fermions, Interacting boson-fermion models

Subject Categories

Physical Sciences and Mathematics

Abstract

We investigate the structure of the permuation orbifolds for the rank three free fermion vertex superalgebra $\mathcal{F}(3)$ (of central charge $\frac{3}{2}$) and the rank three symplectic fermion vertex superalgebra $\mathcal{SF}(3)$ (of central charge -6). We give minimal strong generating sets for the orbifolds $\mathcal{F}(3)^{S_3}$, $\mathcal{F}(3)^{\mathbb{Z}_3}$, $\mathcal{SF}(3)^{S_3}$ and $\mathcal{SF}(3)^{\mathbb{Z}_3}$. In particular, we show the orbifold $\mathcal{F}(3)^{S_3}$ is isomorphic to $\mathcal{F}(1) \otimes W$, where $W$ is $W$-superalgebra of type $(2,4,\frac{9}{2})$. Additionally, we give a bosonic description of the orbifold $\mathcal{F}(3)^{S_3}$. We find analogous isomorphisms for the orbifolds $\mathcal{F}(3)^{\mathbb{Z}_3}$, $\mathcal{SF}(3)^{S_3}$ and $\mathcal{SF}(3)^{\mathbb{Z}_3}$, where the $W$-algebras are type $(1,\frac{9}{2}, \frac{9}{2})$, $(2,3^3,4^3,5^5,6^4)$ and $(2^4,3^4,4^4,5^4)$, respectively. We compute the characters for the orbifolds as well.

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