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 → ∞ limit of three dimensional $$ mathcal{n} $$ = 2 super-gravity [1]. 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 → ∞ limit.