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arXiv · 2110.07794

Carrollian and Galilean conformal higher-spin algebras in any dimensions

Andrea Campoleoni·Simon Pekar
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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 $D=5$.

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Andrea Campoleoni, Simon Pekar. 2022-02-24. Carrollian and Galilean conformal higher-spin algebras in any dimensions. https://doi.org/10.1007/jhep02(2022)150

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