Non-relativistic Chern-Simons supergravity with torsion

A bstract In this work, we construct a three-dimensional non-relativistic Chern-Simons supergravity theory with both curvature and torsion within the Mielke-Baekler framework. We show that a consistent non-relativistic supergravity formulation requires starting from a $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 supersymmetric extension of the Mielke-Baekler algebra and implementing a non-relativistic expansion via the semigroup expansion method, rather than a naive contraction. This procedure allows one to overcome the usual difficulties of non-relativistic supergravity constructions, ensuring closure of the superalgebra and the existence of a non-degenerate invariant bilinear form. The resulting model is characterized by two parameters ( p , q ), which interpolate between different non-relativistic supergravity theories, including the extended Bargmann, Newton-Hooke, and torsional models. Our results provide a unified framework for non-relativistic supergravity with torsion and open new avenues for exploring supersymmetric extensions of Galilean and Carrollian gravity theories.