Newton-Cartan Supergravity

TL;DR

This paper develops a supersymmetric extension of three-dimensional Newton-Cartan gravity by gauging a super-Bargmann algebra, introducing a novel N=2 structure with unique fermionic symmetries and dual potentials.

Contribution

It constructs the first supersymmetric Newton-Cartan gravity model in three dimensions with an N=2 super-Bargmann algebra and explores the role of dual potentials and fermionic symmetries.

Findings

Introduced a super-Bargmann algebra with N=2 supersymmetry.

Demonstrated reduction to a supersymmetric Newton potential.

Identified the necessity of a dual Newton potential for supersymmetry rules.

Abstract

We construct a supersymmetric extension of three-dimensional Newton-Cartan gravity by gauging a super-Bargmann algebra. In order to obtain a non-trivial supersymmetric extension of the Bargmann algebra one needs at least two supersymmetries leading to a N=2 super-Bargmann algebra. Due to the fact that there is a universal Newtonian time, only one of the two supersymmetries can be gauged. The other supersymmetry is realized as a fermionic Stueckelberg symmetry and only survives as a global supersymmetry. We explicitly show how, in the frame of a Galilean observer, the system reduces to a supersymmetric extension of the Newton potential. The corresponding supersymmetry rules can only be defined, provided we also introduce a `dual Newton potential'. We comment on the four-dimensional case.