Gauged AdS-Maxwell algebra and gravity

TL;DR

This paper introduces a deformation of the anti-de Sitter algebra incorporating Maxwell-like generators, constructs a corresponding gravity model, and finds that the additional gauge fields only contribute topologically, leaving Einstein-Cartan gravity unaffected.

Contribution

It presents a novel gauging of the AdS-Maxwell algebra leading to a gravity model with topological Maxwell fields, extending the understanding of algebraic deformations in gravity theories.

Findings

The gauge fields for Maxwell generators are topological and do not affect dynamics.

The model reproduces Einstein-Cartan gravity with Holst term.

Potential extensions could introduce nontrivial Maxwell field dynamics.

Abstract

We deform the anti-de Sitter algebra by adding additional generators $\mathcal{Z}_{ab}$, forming in this way the negative cosmological constant counterpart of the Maxwell algebra. We gauge this algebra and construct a dynamical model with the help of a constrained the BF theory. It turns out that the resulting theory is described by the Einstein-Cartan action with Holst term, and the gauge fields associated with the Maxwell generators $\mathcal{Z}_{ab}$ appear only in topological terms that do not influence dynamical field equations. We briefly comment on the extension of this construction, which would lead to a nontrivial Maxwell fields dynamics.