Matter Coupling and Spontaneous Symmetry Breaking in Topological Gravity

Matter is coupled to three-dimensional gravity such that the topological phase is allowed and the (anti-) de Sitter or Poincar\'e symmetry remains intact. Spontaneous symmetry breaking to the Lorentz group occurs if a scalar field is included. This Higgs field can then be used to couple matter so that the familiar form of the matter coupling is established in the broken phase. We also give the supersymmetrization of this construction.