Weyl SUSY vs Conformal SUSY

Question

Is it possible to add the generators of dilatations to Poincare superalgebra in any dimensions with any number of supercharges without adding the full superconformal generators?

I have only seen superconformal algebras so far but never a Weyl-SUSY algebra that is the bosonic sector only consists of $\{P_a, J_{ab}, D, \text{R-symmetry generator}\}$ but not the generators of special conformal symmetry $\{K_a\}$.

Answer 1

Unitary scale invariant theories are either conformal or indistinguishable from conformal theories on $\mathbf{R}^4$. This means that, for all practical purposes, scale invariance and unitarity imply conformality.

For review see slides "Scale and Conformal Invariance" by Zohar Komargodski.