Carrollian conformal scalar as flat-space singleton

Abstract

We show that, in any space-time dimension, the on-shell (electric) conformal Carrollian scalar can be interpreted as the flat-space limit of the singleton representation of the conformal algebra. In fact, a recently proposed higher-spin algebra for Minkowski spacetime amounts to the Poincaré enveloping algebra on the corresponding module. This higher-spin algebra is a contraction of that entering Vasiliev's equations, which can be constructed analogously from the singleton representation of the conformal algebra. We also show that the higher-spin extension of the Poincaré algebra we consider is a subalgebra of all symmetries of the conformal Carrollian scalar, given by a higher-spin version of the (extended) BMS algebra.

6 pages. Typos corrected and minor clarifications added

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Cited by in corpus (6)

• Carroll/fracton particles and their correspondence
• Symmetry group at future null infinity II: Vector theory
• Manifestly Covariant Worldline Actions from Coadjoint Orbits. Part I: Generalities and Vectorial Descriptions
• Classification of Conformal Carroll Algebras
• Carroll-Schrödinger Equation
• Enhanced Conformal $BM{S}_3$ Symmetries