Rigid Supersymmetric Backgrounds of 3-dimensional Newton-Cartan Supergravity

Recently, a non-relativistic off-shell formulation of three dimensional Newton-Cartan supergravity was proposed as the $c\to \mathrm{\infty }$ limit of three dimensional $\mathcal{N}=2$ supergravity in arXiv:1505.02095. In the present paper we study supersymmetric backgrounds within this theory. Using integrability constraints for the non-relativistic Killing spinor equations, we explicitly construct all maximally supersymmetric solutions, which admit four supercharges. In addition to these solutions, there are $\frac{1}{2}$-BPS solutions with reduced supersymmetry. We give explicit examples of such backgrounds and derive necessary conditions for backgrounds preserving two supercharges. Finally, we address how supersymmetric backgrounds of $\mathcal{N}=2$ supergravity are connected to the solutions found here in the $c\to \mathrm{\infty }$ limit.