2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55531We study higher--derivative supergravity with curvature squared terms in different bases. Performing a Weyl rescaling only on the metric or on all the superfield components does not allow to obtain a normalized kinetic Einstein term from a $\cR+\cR^2$ theory. It is necessary to combine a Legendre transformation and a Weyl rescaling on a $\cR+\cR^2$ theory to arrive at a theory of supergravity coupled to matter. This mechanism is applied to supergravity coupled to a general function $k(R,\BR,Φ,\barΦ)$, where $R$ is one of the supergravity chiral superfields and $Φ$ a chiral matter superfield.17 pages LateX file, no figuresHigh Energy Physics - Theorytext