Anti de Sitter Gravity from BF-Chern-Simons-Higgs Theories

TL;DR

This paper demonstrates how a BF-Chern-Simons inspired action based on the AdS_4 isometry group can reproduce gravity with a cosmological constant and Gauss-Bonnet term, and explores extending this to higher-spin theories.

Contribution

It introduces a novel action framework inspired by BF and Chern-Simons models that reproduces known gravity actions and discusses initial steps for higher-spin extensions in AdS_4.

Findings

Reproduces MacDowell-Mansouri gravity action from BF-Chern-Simons inspired model

Identifies AdS_4 as a natural vacuum of the theory

Proposes preliminary steps for higher-spin extension in AdS_4

Abstract

It is shown that an action inspired from a BF and Chern-Simons model, based on the $AdS_4$ isometry group SO(3, 2), with the inclusion of a Higgs potential term, furnishes the MacDowell-Mansouri-Chamseddine-West action for gravity, with a Gauss-Bonnet and cosmological constant term. The $AdS_4$ space is a natural vacuum of the theory. Using Vasiliev's procedure to construct higher spin massless fields in AdS spaces and a suitable star product, we discuss the preliminary steps to construct the corresponding higher-spin action in $AdS_4$ space representing the higher spin extension of this model. Brief remarks on Noncommutative Gravity are made.