Interactions in MacDowell-Mansouri Gravitation

TL;DR

This thesis investigates the coupling of matter fields in MacDowell-Mansouri gravity, revealing limitations in achieving a unified gauge-theoretic formulation due to auxiliary field requirements.

Contribution

It analyzes possible kinetic terms and couplings in MacDowell-Mansouri gravity, highlighting obstructions and the challenges in aligning gravity with Yang-Mills theories.

Findings

Interactions mostly unaffected except for scalar fields

Obstructions due to auxiliary fields needed for covariance

Theory cannot fully unify gravity with Yang-Mills frameworks

Abstract

In this bachelor thesis, possible kinetic terms and couplings of standard fields in MacDowell-Mansouri-Stelle-West gravity are studied with some aspects of group theory in mind. Possible obstructions to these couplings are considered and used to make statements about the validity of the theory when coupled to matter. While interactions themselves turn out to be mostly unaffected except for scalar fields, the theory fails at its goal of putting gravity on equal footing with Yang-Mills theories. This happens with the kinetic term for spin-1 gauge fields and spin-0 ones, as one needs auxiliary fields to ensure manifest covariance with respect to the internal group $ SO(2,3) $.