# Does scale invariance and R-invariance of Kähler potential imply superconformal symmetry?

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?

• Analogous non-SUSY question: physics.stackexchange.com/q/6384/2451 – Qmechanic Nov 18 '16 at 11:10
• I am aware of the subtlety of the question in the general case, but I'm persuaded SUSY saves the day and $R_K = 0$ is enough to move from dilations to the superconformal group, though I cannot manage a proof. – Riccardo Antonelli Nov 18 '16 at 15:25