Aspects of higher spin symmetry in flat space

Abstract

We review some aspects of higher spin symmetry, in (Anti-)de Sitter and flat space–times, aiming at closing the gap between the constantly curved and flat cases. On (Anti-)de Sitter space, non-Abelian higher spin algebras are at the core of the construction of interacting theories of higher spin gravity. By considering a suitable contraction of these algebras, we show that similar considerations can apply to Minkowski space–time. We identify a unique candidate to the role of higher spin symmetry in flat space that can also be built as a quotient of the universal enveloping algebra of the isometries of the vacuum, as in the (Anti-)de Sitter case. We then show how to recover the free dynamics from the gauging of the resulting algebra at the linear level. Finally, we show how to realise this gauge algebra as a subset of the global symmetries of a Carrollian conformal scalar field theory living on the null infinity of Minkowski space–time. This theory emerges as the limit of vanishing speed of light of a free massless relativistic scalar. The identification of the same higher spin algebra that rules the dynamics in the bulk of space–time within the global symmetries of this boundary theory paves the way to a flat counterpart of higher spin holography.