The fact that a QFT in 3+1d is scale invariant does not automatically imply that the QFT is also invariant under the full conformal group, cf. e.g. this Phys.SE post. Counterexamples are known, but as far as I know are all non-supersymmetric QFTs.
I would like to ask if considering a supersymmetric QFT in 3+1d, scale invariance implies conformal invariance. If yes, what is the argument? If no, what is a known counterexample?
I don't know if the question is studied, or is an open problem. Second question would be if the answer changes with the ammount of supersymmetry we choose.