Three-Dimensional Extended Lifshitz, Schr\"odinger and Newton-Hooke Supergravity

TL;DR

This paper systematically analyzes three-dimensional N=2 extended Bargmann superalgebra and its extensions, constructing corresponding supergravity actions using invariant bilinear forms, advancing the understanding of non-relativistic supergravity theories.

Contribution

It introduces a systematic approach to extend the N=2 superalgebra and constructs new supergravity actions based on invariant bilinear forms.

Findings

Constructed Chern-Simons supergravity actions for extended Bargmann, Newton-Hooke, Lifshitz, and Schr"odinger superalgebras.

Identified invariant non-degenerate bilinear forms for these algebras.

Provided a unified framework for non-relativistic supergravity theories in three dimensions.

Abstract

We provide a systematic analysis of three-dimensional N = 2 extended Bargmann superalgebra and its Newton-Hooke, Lifshitz and Schr\"odinger extensions. These algebras admit invariant non-degenerate bi-linear forms which we utilized to construct corresponding Chern-Simons supergravity actions.