Interactions in MacDowell-Mansouri Gravitation

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) $.