  We give an explicit example of a model in D=4-epsilon space-time dimensions
that is scale but not conformally invariant, is unitary, and has finite
correlators. The invariance is associated with a limit cycle renormalization
group (RG) trajectory. We also prove, to second order in the loop expansion, in
D=4-epsilon, that scale implies conformal invariance for models of any number
of real scalars. For models with one real scalar and any number of Weyl spinors
we show that scale implies conformal invariance to all orders in perturbation
theory.
