Three-Dimensional Extended Bargmann Supergravity

We show that three-dimensional general relativity, augmented with two vector fields, allows for a nonrelativistic limit, different from the standard limit leading to Newtonian gravity, that results in a well-defined action which is of the Chern-Simons type. We show that this three-dimensional "extended Bargmann gravity," after coupling to matter, leads to equations of motion allowing a wider class of background geometries than the ones that one encounters in Newtonian gravity. We give the super-symmetric generalization of these results and point out an important application in the context of calculating partition functions of nonrelativistic field theories using localization techniques.