Three-dimensional teleparallel Chern-Simons supergravity theory

Abstract: In this work we present a gauge-invariant three-dimensional teleparallel supergravity theory using the Chern-Simons formalism. The present construction is based on a supersymmetric extension of a particular deformation of the Poincar\'e algebra. At the bosonic level the theory describes a non-Riemannian geometry with a non-vanishing torsion. In presence of supersymmetry, the teleparallel supergravity theory is characterized by a non-vanishing super-torsion in which the cosmological constant can be seen as a source for the torsion. We show that the teleparallel supergravity theory presented here reproduces the Poincar\'e supergravity in the vanishing cosmological limit. The extension of our results to $\mathcal{N}=p+q$ supersymmetries is also explored.