Cosets, characters and fusion for admissible-level $\mathfrak{osp}(1|2)$ minimal models

Abstract

We study the minimal models associated to $\mathfrak{osp}(1|2)$, otherwise known as the fractional-level Wess-Zumino-Witten models of $\mathfrak{osp}(1|2)$. Since these minimal models are extensions of the tensor product of certain Virasoro and ${\mathfrak{sl}}_2$ minimal models, we can induce the known structures of the representations of the latter models to get a rather complete understanding of the minimal models of $\mathfrak{osp}(1|2)$. In particular, we classify the irreducible relaxed highest-weight modules, determine their characters and compute their Grothendieck fusion rules. We also discuss conjectures for their (genuine) fusion products and the projective covers of the irreducibles.

arXiv comment26 pages, minor revision

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• Gluing vertex algebras
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• Braided Tensor Categories related to ${\mathcal{B}}_p$ Vertex Algebras
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• Boundary vertex algebras for 3d $\mathcal{N}=4$ rank-0 SCFTs
• Classifying relaxed highest-weight modules for admissible-level Bershadsky-Polyakov algebras
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• Tensor Categories arising from the Virasoro Algebra
• Three Dimensional Topological Field Theories and Nahm Sum Formulas
• Staggered modules of $N=2$ superconformal minimal models
• Fusion rules and rigidity for weight modules over the simple admissible affine $\mathfrak{sl}(2)$ and $\mathcal{N}=2$ superconformal vertex operator superalgebras
• $A_{2l}^{(2)}$ at level $-l-\frac{1}{2}$