Three-dimensional supergravity reloaded

The locally supersymmetric extension of the most general gravity theory in three dimensions leading to first-order field equations for the vielbein and the spin connection is constructed. Apart from the Einstein-Hilbert term with cosmological constant, the gravitational sector contains the Lorentz-Chern-Simons form and a term involving the torsion each with arbitrary couplings. The supersymmetric extension is carried out for vanishing and negative effective cosmological constant, and it is shown that the action can be written as a Chern-Simons theory for the supersymmetric extension of the Poincare and AdS groups, respectively. Here we introduce a duality map between different gravity theories that greatly simplifies the construction. This map relies on the different ways to make geometry emerge from a single gauge potential. The extension for N = p + q gravitini is also performed.