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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?

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  • $\begingroup$ Analogous non-SUSY question: physics.stackexchange.com/q/6384/2451 $\endgroup$ – Qmechanic Nov 18 '16 at 11:10
  • $\begingroup$ 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. $\endgroup$ – Riccardo Antonelli Nov 18 '16 at 15:25

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