Non-relativistic Chern-Simons supergravity with torsion

[摘要] 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 N\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ \mathcal{N} $$\end{document} = 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.

[发布日期] 2026-08-03

[关键词] Supergravity Models;Chern-Simons Theories;Gauge Symmetry;Classical Theories of Gravity