Gauge theory of the Maxwell and semi-simple extended (anti) de Sitter algebra

TL;DR

This paper constructs a gauge-invariant model based on a semi-simple and Maxwell extended (anti) de Sitter algebra, leading to an extended Einstein's equations and a unification of gravity with Maxwell symmetries in higher dimensions.

Contribution

It introduces a novel gauge-invariant model using Maxwell semi-simple extension of (anti) de Sitter algebra, incorporating spontaneous symmetry breaking and deriving extended Einstein equations.

Findings

Derived a five-dimensional Stelle-West like model with symmetry breaking effects.

Established a MacDowell-Mansouri like action including Maxwell extension terms.

Showed equivalence of models under specific gauge conditions.

Abstract

In this paper, a semi-simple and Maxwell extension of the (anti) de Sitter algebra is constructed. Then, a gauge-invariant model has been presented by gauging the Maxwell semi-simple extension of the (anti) de Sitter algebra. We firstly construct a Stelle-West like model action for five-dimensional space-time in which the effects of spontaneous symmetry breaking have been taken into account. In doing so, we get an extended version of Einstein's field equations. Next, we decompose the five-dimensional extended Lie algebra and establish a MacDowell-Mansouri like action that contains the Einstein-Hilbert term, the cosmological term as well as new terms coming from Maxwell extension in four-dimensional space-time where the torsion-free condition is assumed. Finally, we have shown that both models are equivalent for an appropriately chosen gauge condition.