Consider a four-dimensional $\mathcal{N} = 1$ field theory with Lagrangian:
$ \mathcal{L} = \int d^4 \theta K(\Phi, \bar \Phi) $
and assume $K$ transforms well under dilations with scaling dimension $2$ (so that the action is scale-invariant) and is invariant under R-charge.
Is this sufficient to deduce the theory is conformal (and thus superconformal)? If so, how would this be proven?
