Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity

TL;DR

This paper develops new non-relativistic and Carrollian algebra extensions of (A)dS symmetries, constructs associated Chern-Simons gravity theories in 3D, and explores their embedding in affine Kac-Moody algebras, enriching the landscape of non-relativistic gravity models.

Contribution

It introduces finite- and infinite-dimensional non-relativistic algebra extensions of (A)dS symmetries and constructs corresponding Chern-Simons gravity actions, expanding the framework of non-relativistic gravity theories.

Findings

Constructed non-relativistic algebra extensions from (A)dS algebras.

Embedded these algebras in affine Kac-Moody algebras.

Developed Chern-Simons gravity theories invariant under these symmetries.

Abstract

We construct finite- and infinite-dimensional non-relativistic extensions of the Newton-Hooke and Carroll (A)dS algebras using the algebra expansion method, starting from the (anti-)de Sitter relativistic algebra in D dimensions. These algebras are also shown to be embedded in different affine Kac-Moody algebras. In the three-dimensional case, we construct Chern-Simons actions invariant under these symmetries. This leads to a sequence of non-relativistic gravity theories, where the simplest examples correspond to extended Newton-Hooke and extended (post-)Newtonian gravity together with their Carrollian counterparts.