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arXiv · 2604.24615

Non-Relativistic Chern-Simons Supergravity with Torsion

Francisco Barriga·Patrick Concha·Nelson Merino·Evelyn Rodríguez
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Abstract

In this work, we construct a three-dimensional non-relativistic Chern--Simons supergravity theory with both curvature and torsion within the Mielke--Baekler framework. We show that a consistent non-relativistic supergravity formulation requires starting from a $\mathcal{N}=2$ supersymmetric extension of the Mielke--Baekler algebra and implementing a non-relativistic expansion via the semigroup expansion method, rather than a naive contraction. This procedure allows one to overcome the usual difficulties of non-relativistic supergravity constructions, ensuring closure of the superalgebra and the existence of a non-degenerate invariant bilinear form. The resulting model is characterized by two parameters $(p,q)$, which interpolate between different non-relativistic supergravity theories, including the extended Bargmann, Newton--Hooke, and torsional models. Our results provide a unified framework for non-relativistic supergravity with torsion and open new avenues for exploring supersymmetric extensions of Galilean and Carrollian gravity theories.

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Francisco Barriga, Patrick Concha, Nelson Merino, Evelyn Rodríguez. 2026-04-27. Non-Relativistic Chern-Simons Supergravity with Torsion. https://arxiv.org/abs/2604.24615

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