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

TL;DR

This paper analyzes the structure of minimal models related to the affine superalgebra $rak{osp}(1|2)$, classifying modules, computing characters, and exploring fusion rules to deepen understanding of these fractional-level models.

Contribution

It provides a classification of irreducible relaxed highest-weight modules, character formulas, and fusion rules for $rak{osp}(1|2)$ minimal models, extending known structures from related models.

Findings

Classified irreducible relaxed highest-weight modules.

Determined characters of modules.

Computed Grothendieck fusion rules.

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.