Symplectic critical models in $6+\epsilon$ dimensions

We consider nontrivial critical models in $d=6+\epsilon$ spacetime dimensions with anticommuting scalars transforming under the symplectic group $\text{Sp}(N)$. These models are nonunitary, but the couplings are real and all operator dimensions are positive. At large $N$ we can take $\epsilon\to1$ consistently with the loop expansion and thus provide evidence that these theories may be used to define critical models in $d=7$. The relation of these theories to critical $\text{Sp}(N)$ theories, defined similarly to the well-known critical $\text{O}(N)$ theories, is examined, and some similarities are pointed out.