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Boundary States and Anomalous Symmetries of Fermionic Minimal Models

The fermionic minimal models are a recently-introduced family of two-dimensional spin conformal field theories. We determine all of their conformal boundary states and potentially anomalous $\mathbb{Z}_2$ global symmetries. The latter task hinges upon on a conjecture about $\mathfrak{su}(2)$ affine parities generalising an earlier result known to have an interpretation in terms of Fermat curves. Our results indicate a close connection between several properties of the models, including the matching of the sizes of the SPT classes of boundary states, the existence of anomalous $\mathbb{Z}_2$ symmetries, and the vanishing of the Ramond-Ramond sector, for which we provide an explanation.