The Non-Relativistic 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 non-relativistic superparticle with the relativistic kappa-symmetric three-dimensional superparticle.