# Chern-Simons--Antoniadis-Savvidy forms and standard supergravity

## TL;DR

This paper constructs a four-dimensional supergravity action based on ChSAS forms and Maxwell superalgebra, introducing a method to decompose the action into bulk and boundary parts reflecting the algebra's structure.

## Contribution

It develops a novel approach using FDA decomposition and the Extended Cartan Homotopy Formula to analyze ChSAS supergravity actions and their subspace structures.

## Key findings

- Successfully constructed a supergravity action for Maxwell superalgebra.
- Provided a method to separate bulk and boundary contributions in ChSAS actions.
- Demonstrated splitting of the Lagrangian according to algebraic subspaces.

## Abstract

In the context of the so called the Chern--Simons--Antoniadis--Savvidy (ChSAS) forms, we use the methods for FDA decomposition in 1-forms to construct a four-dimensional ChSAS supergravity action for the Maxwell superalgebra. On the another hand, we use the Extended Cartan Homotopy Formula to find a method that allows the separation of the ChSAS action into bulk and boundary contributions and permits the splitting of the bulk Lagrangian into pieces that reflect the particular subspace structure of the gauge algebra.