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

Thomas Creutzig; Shashank Kanade; Tianshu Liu; David Ridout

doi:10.1016/j.nuclphysb.2018.10.022

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arXiv · 1806.09146

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

Thomas Creutzig·Shashank Kanade·Tianshu Liu·David Ridout

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Abstract

We study the minimal models associated to $\mathfrak{osp}(1 \vert 2)$, otherwise known as the fractional-level Wess-Zumino-Witten models of $\mathfrak{osp}(1 \vert 2)$. 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 $\mathfrak{osp}(1 \vert 2)$. 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.

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Thomas Creutzig, Shashank Kanade, Tianshu Liu, David Ridout. 2018-06-24. Cosets, characters and fusion for admissible-level $\mathfrak{osp}(1 \vert 2)$ minimal models. https://doi.org/10.1016/j.nuclphysb.2018.10.022

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