Newton-Cartan supergravity with torsion and Schrödinger supergravity

Abstract

We derive a torsionfull version of three-dimensional N=2 Newton-Cartan supergravity using a non-relativistic notion of the superconformal tensor calculus. The "superconformal" theory that we start with is Schrödinger supergravity which we obtain by gauging the Schrödinger superalgebra. We present two non-relativistic N=2 matter multiplets that can be used as compensators in the superconformal calculus. They lead to two different off-shell formulations which, in analogy with the relativistic case, we call "old minimal" and "new minimal" Newton-Cartan supergravity. We find similarities but also point out some differences with respect to the relativistic case.

30 pages

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• A Schrödinger approach to Newton-Cartan and Hořava-Lifshitz gravities
• Three-dimensional exotic Newtonian gravity with cosmological constant
• Generalized Maxwellian exotic Bargmann gravity theory in three spacetime dimensions
• Three-dimensional Poincaré supergravity and $\mathcal{N}$-extended supersymmetric BMS${}_3$ algebra
• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
• Hamiltonian For String in Newton-Cartan Background
• Resonant superalgebras and $\mathcal{N}=1$ supergravity theories in three spacetime dimensions
• Symmetries and Couplings of Non-Relativistic Electrodynamics
• Galilean Geometry in Condensed Matter Systems
• A pedagogical review of gravity as a gauge theory