Newton-Cartan supergravity with torsion and Schrödinger supergravity

Abstract

We derive a torsionfull version of three-dimensional $$ \mathcal{N}=2 $$ 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 $$ \mathcal{N}=2 $$ 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.