Newton-Cartan (super)gravity as a non-relativistic limit
Eric Bergshoeff, Jan Rosseel, Thomas Zojer
TL;DR
The paper develops a systematic contraction-based limiting procedure to obtain non-relativistic (super)gravity from relativistic theories, applied by taking $\omega \to \infty$ in appropriately redefined vielbeins, spin-connections, and supermultiplets. This approach faithfully reproduces Newton–Cartan gravity as a non-relativistic limit of General Relativity and extends to supersymmetric settings, yielding a new off-shell formulation of three-dimensional Newton–Cartan supergravity that includes a real auxiliary scalar $S$. It also demonstrates the method on a non-relativistic superparticle in curved backgrounds, and shows that the procedure can produce off-shell non-relativistic multiplets not accessible via standard gauging. The work thus provides a versatile bridge between relativistic and non-relativistic geometries, with potential implications for non-relativistic holography, localization of non-relativistic SUSY theories, and higher-dimensional generalizations or matter couplings.
Abstract
We define a procedure that, starting from a relativistic theory of supergravity, leads to a consistent, non-relativistic version thereof. As a first application we use this limiting procedure to show how the Newton-Cartan formulation of non-relativistic gravity can be obtained from general relativity. Then we apply it in a supersymmetric case and derive a novel, non-relativistic, off-shell formulation of three-dimensional Newton-Cartan supergravity.