Three-Dimensional Extended Bargmann Supergravity

TL;DR

This paper introduces a new three-dimensional non-relativistic gravity theory called Extended Bargmann Gravity, derived from General Relativity with additional fields, which admits a broader class of backgrounds and has applications in non-relativistic quantum field theory.

Contribution

It presents a novel non-relativistic limit of 3D General Relativity leading to a Chern-Simons type action, extending Newtonian gravity and including supersymmetric generalizations.

Findings

Allows for a wider class of background geometries than Newtonian gravity.

Provides a supersymmetric extension of the theory.

Facilitates calculations of partition functions in non-relativistic field theories.

Abstract

We show that three-dimensional General Relativity, augmented with two vector fields, allows for a non-relativistic limit, different from the standard limit leading to Newtonian gravity, that results into 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 supersymmetric generalization of these results and point out an important application in the context of calculating partition functions of non-relativistic field theories using localization techniques.