Dual Description of Supergravity MacDowell-Mansouri Theory
In the context of field theory two elements seem to be necessary to search for strong-weak coupling duality. First, a gauge theory formulation and second, supersymmetry. For gravitation these two elements are present in MacDowell-Mansouri supergravity. The search for an "effective duality" in this theory presents technical and conceptual problems that we discuss. Nevertheless, by means of a field theoretical approach, which in the abelian case coincides with $S$-duality, we exhibit a dual theory, with inverted couplings. This results in a supersymmetric non-linear sigma model of the Freedman-Townsend type.