Newton-Cartan supergravity with torsion and Schrodinger supergravity

We derive a torsionfull version of three-dimensional N - 2 Newton-Cartan supergravity using a non-relativistic notion of the superconformal tensor calculus. The superconformal theory that we start with is Schrodinger supergravity which we obtain by gauging the Schrodinger superalgebra. We present two non-relativistic N = 2 matter multiplets that can be used as compensators in the superconformal calculus. They lead to two different off -shell formulations which, in analogy with the relativistic case, we call old minimal and new minimal Newton-Cartan supergravity. We find similarities but also point out some differences with respect to the relativistic case.