Constraints on Long-Range Forces in De Sitter Space

TL;DR

This paper uses boundary symmetry constraints to analyze the consistency of partially massless fields in de Sitter space, showing that certain couplings are forbidden unless an infinite tower of higher-spin fields is included.

Contribution

It introduces a boundary symmetry-based framework to test the consistency of partially massless fields coupled to gravity in de Sitter space, revealing necessary conditions for their viability.

Findings

PM fields of spin 2 or 3 cannot couple consistently to gravity in 4D without additional fields.

In higher dimensions, consistent couplings are possible with more PM fields, satisfying unitarity.

An infinite tower of higher-spin PM fields may be required for full consistency.

Abstract

The representation theory of de Sitter space admits partially massless (PM) particles, but whether such particles can participate in consistent interacting theories remains unclear. We investigate the consistency of theories containing PM fields, particularly when these fields are coupled to gravity. Our strategy exploits the fact that PM fields correspond to partially conserved currents on the spacetime boundary, which generate symmetries. These symmetries place stringent constraints on correlation functions of charged operators, allowing us to test the consistency of a proposed bulk spectrum. When the assumed operator content violates these constraints, the corresponding bulk theory is ruled out. Applying this framework, we show that, in four-dimensional de Sitter space, PM fields of spin 2 or 3 (at depth 0) cannot couple consistently to gravity: such couplings necessitate additional massive fields, which are inevitably non-unitary. In higher dimensions, however, the constraints can be satisfied without violating unitarity if further PM fields are included. The resulting structure leads to additional charge conservation laws, which suggests that consistency may ultimately require an infinite tower of higher-spin PM fields, akin to the situation for ordinary higher-spin symmetries. The methods developed here provide powerful constraints on possible long-range interactions in de Sitter space and delineate the landscape of consistent quantum field theories in cosmological spacetimes.