Non-Lorentzian Supergravity and Kinematical Superalgebras

TL;DR

This paper classifies supersymmetric extensions of non-Lorentzian kinematical algebras and constructs three-dimensional Chern-Simons supergravity theories based on these algebras, advancing non-Lorentzian supergravity models.

Contribution

It introduces a systematic classification of supersymmetric kinematical algebras and develops corresponding non-Lorentzian supergravity theories using expansion procedures.

Findings

Derived diverse kinematical superalgebras via expansion methods.

Built 3D Chern-Simons supergravity models with supersymmetry.

Established non-degenerate invariant bilinear forms for these algebras.

Abstract

In this paper, we present and classify the supersymmetric extensions of extended kinematical algebras, at the basis of non-Lorentzian physics theories. The diverse kinematical superalgebras are here derived by applying non- and ultra-relativistic expansion procedures involving different semigroups. We then build three-dimensional Chern-Simons non-Lorentzian supergravity theories based on such (extended) kinematical superalgebras, providing the supersymmetry transformation laws of the fields and the field equations of the models, which correspond to the vanishing of the curvature two-forms. In fact, the expansion procedure adopted allows to automatically end up with a non-degenerate bilinear invariant trace for the (extended) kinematical superalgebras. The latter is a crucial ingredient of the Chern-Simons field-theoretical formulation, as it allows to include a kinetic term for each gauge field of the theory, implying the vanishing of the curvature two-forms as field equations.