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.
Categories: hep-th