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

## TL;DR

This paper constructs a first-order supergravity action in four dimensions by gauging the Maxwell-Weyl superalgebra, incorporating local scale invariance with a scalar field, and deriving a generalized Einstein equation with a variable cosmological term.

## Contribution

It introduces a novel supergravity model based on the Maxwell-Weyl superalgebra, including a new approach to local scale invariance and a generalized Einstein equation.

## Key findings

- Successful construction of the supergravity action using algebra curvatures
- Implementation of local scale invariance via a compensating scalar field
- Derivation of a generalized Einstein equation with a coordinate-dependent cosmological term

## Abstract

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.