Newton-Cartan supergravity with torsion and Schr\"odinger supergravity

Understand

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 Schr\"odinger supergravity which we obtain by gauging the Schr\"odinger 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.