$D=4$ supergravity from the Maxwell-Weyl superalgebra

Abstract We present the construction of the first-order $D=4$, $\mathcal{N}=1$ supergravity action by gauging the Maxwell-Weyl superalgebra. The four-form lagrangian is constructed by using the curvatures of the algebra and the local scale invariance of the action is achieved through the introduction of a compensating scalar field. Finally, we find the generalized Einstein equation with a coordinate dependent cosmological term.