Towards higher-spin holography in flat space

TL;DR

This paper explores the algebraic structure of higher-spin symmetries in 4d Minkowski space, proposing a flat space holography framework by constructing a singleton representation analogous to AdS higher-spin theories.

Contribution

It introduces a novel flat space higher-spin algebra as a deformation of the Poincare algebra and constructs explicit singleton representations, advancing flat space holography understanding.

Findings

Constructed the chiral flat space higher-spin algebra as a quotient of the universal enveloping algebra.

Identified and explicitly realized the flat space singleton representation in spinor and oscillator form.

Provided insights into the properties of the singleton, supporting flat space holography models.

Abstract

We study the chiral flat space higher-spin algebra, which is the global symmetry algebra of the chiral higher-spin theory in the 4d Minkowski space. We find that it can be constructed as the universal enveloping algebra of a certain chiral deformation of the Poincare algebra quotiented by a set of quadratic identities. These identities allow us to identify a representation of the latter algebra, which by analogy with the AdS space higher-spin holography, we interpret as the flat space singleton representation. We provide two explicit realisations of this singleton representation -- in terms of $sl(2,\mathbb{C})$ spinors and in terms of oscillator-like variables -- as well as briefly discuss its properties.