title: No-go theorems for unitary and interacting partially massless spin-two fields.
abstract: We examine the generic theory of a paratially 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.
authors.affiliation: AstroParticule et Cosmologie, Unité Mixte de Recherche 7164 du CNRS, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France.
authors.forename: Euihun
authors.initials: E
authors.lastname: Joung
authors.affiliation: AstroParticule et Cosmologie, Unité Mixte de Recherche 7164 du CNRS, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France.
authors.forename: Wenliang
authors.initials: W
authors.lastname: Li
authors.affiliation: Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Am Mühlenberg 1, 14476 Golm, Germany and Kavli Institute for Theoretical Physics China, CAS, Beijing 100190, People's Republic of China.
authors.forename: Massimo
authors.initials: M
authors.lastname: Taronna