Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories

TL;DR

This paper develops new non-relativistic and ultra-relativistic spin-3 gravity algebras using Lie algebra expansion methods, leading to novel gravity theories with potential applications in high-energy physics.

Contribution

It introduces a systematic expansion approach to derive spin-3 extensions of various non-relativistic and ultra-relativistic algebras, including infinite-dimensional families.

Findings

Derived new spin-3 extensions of Newton-Hooke and AdS-Carroll algebras.

Constructed corresponding Chern-Simons gravity actions.

Recovered spin-3 extensions of Galilean and Carroll gravity in the flat limit.

Abstract

In this paper, we present novel and known non-relativistic and ultra-relativistic spin-3 algebras, by considering the Lie algebra expansion method. We start by applying the expansion procedure using different semigroups to the spin-3 extension of the AdS algebra, leading to spin-3 extensions of known non-relativistic and ultra-relativistic algebras. We then generalize the procedure considering an infinite-dimensional semigroup, which allows to obtain a spin-3 extension of two new infinite families of the Newton-Hooke type and AdS-Carroll type. We also present the construction of the gravity theories based on the aforementioned algebras. In particular, the expansion method based on semigroups also allows to derive the (non-degenerate) invariant bilinear forms, ensuring the proper construction of the Chern-Simons gravity actions. Interestingly, in the vanishing cosmological constant limit we recover the spin-3 extensions of the infinite-dimensional Galilean and infinite-dimensional Carroll gravity theories.