Rigid Supersymmetric Backgrounds of 3-dimensional Newton-Cartan Supergravity

Abstract

Recently, a non-relativistic off-shell formulation of three dimensional Newton-Cartan supergravity was proposed as the $c\to \infty$ 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 $c\to \infty$ limit.

26 pages + 2 appendices, 2 figures; v2: references added, clarified which N=2 supergravity theory is being considered; v3: reference added; added clarification and explicit solutions to relativistic integrability conditions

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Cited by in corpus (7)

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• Supersymmetric solutions of $N=(2,0)$ Topologically Massive Supergravity
• Non-Relativistic Supersymmetry on Curved Three-Manifolds
• Minimal $\mathcal{N}=4$ topologically massive supergravity
• Symmetries and Couplings of Non-Relativistic Electrodynamics
• Galilean Geometry in Condensed Matter Systems
• Warped anti-de Sitter in 3d (2,0) Supergravity