Rigid Supersymmetric Backgrounds of 3-dimensional Newton-Cartan Supergravity

TL;DR

This paper classifies supersymmetric backgrounds in three-dimensional Newton-Cartan supergravity, identifying maximally supersymmetric and partially supersymmetric solutions, and explores their relation to relativistic supergravity backgrounds.

Contribution

It provides the first explicit construction and classification of supersymmetric backgrounds in 3D Newton-Cartan supergravity, including maximally and partially supersymmetric solutions.

Findings

Explicit maximally supersymmetric solutions with four supercharges.

Examples of half-BPS backgrounds with reduced supersymmetry.

Necessary conditions for backgrounds preserving two supercharges.

Abstract

Recently, a non-relativistic off-shell formulation of three dimensional Newton-Cartan supergravity was proposed as the $c \rightarrow \infty$ limit of three dimensional $\mathcal{N}=2$ supergravity in arXiv:1505.02095. In the present paper we study supersymmetric backgrounds within this theory. Using integrability constraints for the non-relativistic Killing spinor equations, we explicitly construct all maximally supersymmetric solutions, which admit four supercharges. In addition to these solutions, there are $\frac{1}{2}$-BPS solutions with reduced supersymmetry. We give explicit examples of such backgrounds and derive necessary conditions for backgrounds preserving two supercharges. Finally, we address how supersymmetric backgrounds of $\mathcal{N}=2$ supergravity are connected to the solutions found here in the $c \rightarrow \infty$ limit.