Non-Relativistic Maxwell Chern-Simons Gravity

TL;DR

The paper studies the non-relativistic ($2+1$) limit of Maxwell CS gravity and shows that a finite NR CS theory can be obtained only after enlarging the field content or adopting Maxwellian extensions. It identifies three NR algebras via Inönü–Wigner contractions: an Exotic NR Maxwell algebra with a degenerate bilinear form, a Bargmann NR Maxwell algebra with a non-degenerate form, and a Maxwellian Exotic Bargmann gravity with a richer NR sector and non-degenerate form. The work provides explicit NR CS actions for these algebras and analyzes their field equations, finding fully determinate dynamics in the Bargmann and Maxwellian cases and a partially determinate dynamics in the exotic NR case. These results illuminate how extra U(1) fields and central extensions stabilize NR contractions and open avenues for second-order formulations and potential supersymmetric extensions in non-relativistic gravity models.

Abstract

We consider a non-relativistic (NR) limit of $(2+1)$-dimensional Maxwell Chern-Simons (CS) gravity with gauge algebra [Maxwell] $\oplus \ u(1)\oplus u(1)$. We obtain a finite NR CS gravity with a degenerate invariant bilinear form. We find two ways out of this difficulty: To consider i) [Maxwell] $\oplus\ u(1)$, which does not contain Extended Bargmann gravity (EBG); or, ii) the NR limit of [Maxwell] $\oplus\ u(1)\oplus u(1)\oplus u(1)$, which is a Maxwellian generalization of the EBG.