Carrollian conformal scalar as flat-space singleton

TL;DR

This paper demonstrates that the conformal Carrollian scalar in flat spacetime can be viewed as a limit of the singleton representation, connecting higher-spin algebras with flat-space symmetries and BMS extensions.

Contribution

It establishes a novel interpretation of the Carrollian scalar as a flat-space singleton and links higher-spin algebras with extended BMS symmetries in this context.

Findings

Conformal Carrollian scalar is the flat-space limit of the singleton representation.

Higher-spin algebra in Minkowski space is a contraction of Vasiliev's algebra.

The extended Poincaré algebra is a subalgebra of the conformal Carrollian scalar symmetries.

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 Poincar\'e 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 Poincar\'e 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.