Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions

Understand

Einstein gravity in both 3 and 4 dimensions, as well as some interesting generalizations, can be written as gauge theories in which the connection is a Cartan connection for geometry modeled on a symmetric space.

• The relevant models in 3 dimensions include Einstein gravity in Chern-Simons form, as well as a new formulation of topologically massive gravity, with arbitrary cosmological constant, as a single constrained Chern-Simons action.
• In 4 dimensions the main model of interest is MacDowell-Mansouri gravity, generalized to include the Immirzi parameter in a natural way.
• I formulate these theories in Cartan geometric language, emphasizing also the role played by the symmetric space structure of the model.