Carrollian and Galilean conformal higher-spin algebras in any dimensions

TL;DR

This paper constructs and analyzes higher-spin algebras with Poincaré, Carrollian, and Galilean conformal symmetries across various dimensions, revealing their relations via contractions and quotients of universal enveloping algebras.

Contribution

It introduces new higher-spin algebras with specific symmetry properties and demonstrates their derivation as contractions or quotients, extending understanding of higher-spin symmetries in different spacetime limits.

Findings

Higher-spin algebras can be obtained as quotients of universal enveloping algebras.

Contractions relate flat-space, Carrollian, and Galilean higher-spin symmetries.

Special features are identified for the case D=5.

Abstract

We present higher-spin algebras containing a Poincar\'e subalgebra and with the same set of generators as the Lie algebras that are relevant to Vasiliev's equations in any space-time dimension $D \geq 3$. Given these properties, they can be considered either as candidate rigid symmetries for higher-spin gauge theories in Minkowski space or as Carrollian conformal higher-spin symmetries in one less dimension. We build these Lie algebras as quotients of the universal enveloping algebra of $iso(1,D-1)$ and we show how to recover them as In\"on\"u-Wigner contractions of the rigid symmetries of higher-spin gauge theories in Anti de Sitter space or, equivalently, of relativistic conformal higher-spin symmetries. We use the same techniques to also define higher-spin algebras with the same set of generators and containing a Galilean conformal subalgebra, to be interpreted as non-relativistic limits of the conformal symmetries of a free scalar field. We begin by showing that the known flat-space higher-spin algebras in three dimensions can be obtained as quotients of the universal enveloping algebra of $iso(1,2)$ and then we extend the analysis along the same lines to a generic number of space-time dimensions. We also discuss the peculiarities that emerge for $D=5$.