Symplectic critical models in 6 + ϵ dimensions

We consider nontrivial critical models in d=6+ϵd=6+ϵ spacetime dimensions with anticommuting scalars transforming under the symplectic group Sp(N)Sp(N). These models are nonunitary, but the couplings are real and all operator dimensions are positive. At large N   we can take ϵ→1ϵ→1 consistently with the loop expansion and thus provide evidence that these theories may be used to define critical models in d=7d=7. The relation of these theories to critical Sp(N)Sp(N) theories, defined similarly to the well-known critical O(N)O(N) theories, is examined, and some similarities are pointed out.