Carrollian and Galilean conformal higher-spin algebras in any dimensions

TL;DR

This work classifies and constructs higher-spin algebras in flat (Minkowski) and Carrollian/Galilean limits that share the same generator set as Eastwood–Vasiliev algebras. By quotients of the universal enveloping algebra of iso(1,D−1) and gca(D−1), and via Inönü–Wigner contractions from AdS or conformal higher-spin algebras, the authors obtain a family of algebras in any dimension D≥3, including special one-parameter families in D=3 and D=5. They provide detailed treatments for 3D and 5D, discuss partially-massless extensions via A_D[μ], and explore constructions based on Killing tensors and the Schouten bracket to realize additional, non-unitary higher-spin structures. The work also analyzes consistency conditions, finite-dimensional truncations, and geometric realizations, offering a framework for exploring flat-space higher-spin symmetry, potential holographic interpretations, and non-AdS holography avenues. Overall, it lays a systematic foundation for flat-space, Carrollian, and Galilean higher-spin algebras and their contractions from AdS/conformal counterparts.

Abstract

We present higher-spin algebras containing a Poincaré 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 Inönü-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 $D=5$.