On higher spin symmetries in de Sitter QFTs

TL;DR

This paper explores how higher-spin symmetries in de Sitter quantum field theories impose strong constraints, leading to Gaussian boundary correlators and trivial cosmological spectra, akin to a Coleman-Mandula theorem analogue.

Contribution

It demonstrates that higher-spin symmetries in de Sitter QFTs enforce Gaussian boundary correlators, revealing significant restrictions on the theory's dynamics.

Findings

Boundary operators are asymptotically Gaussian.

Operators have trivial cosmological spectra.

Correlations are only Gaussian near boundaries.

Abstract

We consider the consequences of global higher-spin symmetries in quantum field theories on a fixed de Sitter background of spacetime dimension $D \ge 3$. These symmetries enhance the symmetry group associated with the isometries of the de Sitter background and thus strongly constrain the dynamics of the theory. In particular, we consider the case when a higher spin charge acts linearly on a scalar operator to leading order in a Fefferman-Graham expansion near the future/past conformal boundaries. We show that this implies that the expectation values of the operator inserted near the boundaries are asymptotically Gaussian. Thus, these operators have trivial cosmological spectra, and on global de Sitter these operators have only Gaussian correlations between operators inserted near future/past infinity. The latter result may be interpreted as an analogue of the Coleman-Mandula theorem for QFTs on de Sitter spacetime.