Symplectic critical models in 6+ε dimensions

We consider nontrivial critical models in d = 6 + epsilon spacetime dimensions with anticommuting scalars transforming under the symplectic group Sp(N). These models are nonunitary, but the couplings are real and all operator dimensions are positive. At large Nwe can take epsilon -> 1consistently 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 Sp(N) theories, defined similarly to the well- known critical O(N) theories, is examined, and some similarities are pointed out. (C) 2015 The Author. Published by Elsevier B.V.