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The N=1 Singlet Vertex Superalgebra Sm(1), Scott Richey Sidoli

Legacy Theses & Dissertations (2009 - 2024)

In this work we study the vertex operator superalgebra known as the singlet vertex operator superalgebra, denoted $\overline{SM(1)}$. We are particularly interested in the number theoretic properties of the characters, and supercharacters, of irreducible modules of $\overline{SM(1)}$ as modules over the Neveu-Schwarz and Ramond Lie superalgebras, denoted $\mathfrak{ns}$ and $\mathfrak{R}$, respectively. These characters occur as modular-like forms, namely false and mock theta functions. The $S$- and $T$- transformations are computed and we demonstrate modular invariance of the vector space spanned by these characters and supercharacters. We use a continuous version of the Verlinde formula, introduced by Creutzig and Milas, to …