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These include the $O(n)$ model (symmetry group $O(n)$) and the Potts model (symmetry group $S_Q$). Both models make sense for $n,Q\\in \\mathbb{C}$ and not just $n,Q\\in \\mathbb{N}$, and both give rise to a conformal field theory in the critical limit.\n  Here, we study similar models based on the group $PSU(n)$. 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