# Extended gauge theory and gauged Free Differential Algebras

## TL;DR

This paper demonstrates that extended gauge invariants involving higher degree forms can be systematically constructed using Free Differential Algebras, linking extended gauge theories to algebraic structures.

## Contribution

It shows that the non-abelian gauge theories with p-form potentials can be derived from gauging Free Differential Algebras, providing an algebraic foundation for extended gauge invariants.

## Key findings

- Extended invariants can be constructed from Free Differential Algebras.
- Non-abelian gauge theories with higher p-form potentials are obtained via gauging FDAs.
- Provides an algebraic framework for background-free gauge invariants.

## Abstract

Recently, Antoniadis, Konitopoulos and Savvidy introduced, in the context of the so-called extended gauge theory, a procedure to construct background-free gauge invariants, using non-abelian gauge potentials described by higher degree forms. In this article it is shown that the extended invariants found by Antoniadis, Konitopoulos and Savvidy can be constructed from an algebraic structure known as Free Differential Algebra. In other words, we show that the above mentioned non abelian gauge theory, where the gauge fields are described by p-forms with p>1, can be obtained by gauging Free Differential Algebras.