Nonrelativistic superparticle in a curved background

Using a component formulation, we construct the supersymmetric action for a superparticle in a three-dimensional Newton--Cartan supergravity background and clarify its symmetries. Our construction proceeds by first constructing the superparticle in a flat background. Next, by boosting up the background symmetries, we replace in a first step the flat background by a Galilean supergravity background. In a second step the Galilean supergravity background is replaced by a Newton--Cartan supergravity background. We extend our results by adding a supersymmetric cosmological constant and compare the nonrelativistic superparticle with the relativistic κ-symmetric three-dimensional superparticle.