Three-Dimensional Extended Newtonian (Super)Gravity

TL;DR

The paper develops a three-dimensional non-relativistic gravity model invariant under the central extension of the symmetry group that preserves the Newtonian gravity action. It shows that this extended Newtonian gravity arises as a contraction of a bi-metric theory that sums Lorentzian Einstein gravity and Euclidean gravity, and it is formulated as a Chern-Simons theory with an extended algebra. A supersymmetric completion is provided by enlarging the algebra with five Majorana fermions, yielding extended Newtonian supergravity with explicit supercovariant curvatures and transformation rules. The work discusses matter couplings, demonstrates the absence of propagating local degrees of freedom in this Chern-Simons framework, and outlines prospective extensions to include cosmological constant, exotic variants, scale/Schrödinger symmetries, and higher-derivative or bi-gravity generalizations, highlighting potential applications to non-relativistic field theories on curved backgrounds and localization.

Abstract

We present a three dimensional non-relativistic model of gravity that is invariant under the central extension of the symmetry group that leaves the recently constructed Newtonian gravity action invariant. We show that the model arises from the contraction of a bi-metric model that is the sum of the Einstein gravity in Lorentzian and the Euclidean signatures. We also present the supersymmetric completion of this action which provides one of the very few examples of an action for non-relativistic supergravity.