No-Go Theorems for Unitary and Interacting Partially Massless Spin-Two Fields

TL;DR

This paper proves that a unitary, perturbatively local theory of a partially massless spin-two field interacting with gravity cannot exist in four dimensions, revealing fundamental obstructions in such theories.

Contribution

It demonstrates the non-existence of a unitary, local, interacting partially massless spin-two field theory coupled to gravity in four dimensions, clarifying theoretical constraints.

Findings

No consistent unitary theory with positive kinetic sign

Coupling constant must be purely imaginary for positive sign

PM limit of massive gravity lacks gauge symmetry

Abstract

We examine the generic theory of a partially massless (PM) spin-two field interacting with gravity in four dimensions from a bottom-up perspective. By analyzing the most general form of the Lagrangian, we first show that if such a theory exists, its de Sitter background must admit either so(1, 5) or so(2, 4) global symmetry depending on the relative sign of the kinetic terms: the former for a positive sign the latter for a negative sign. Further analysis reveals that the coupling constant of the PM cubic self-interaction must be fixed with a purely imaginary number in the case of a positive sign. We conclude that there cannot exist a unitary theory of a PM spin-two field coupled to Einstein gravity with a perturbatively local Lagrangian. In the case of a negative sign we recover conformal gravity. As a special case of our analysis, it is shown that the PM limit of massive gravity also lacks the PM gauge symmetry.