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

Euihun Joung, Wenliang Li, and Massimo Taronna
Phys. Rev. Lett. 113, 091101 – Published 27 August 2014

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.

  • Received 19 June 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.091101

© 2014 American Physical Society

Authors & Affiliations

Euihun Joung* and Wenliang Li

  • AstroParticule et Cosmologie, Unité Mixte de Recherche 7164 du CNRS, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France

Massimo Taronna

  • 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

  • *joung@apc.univ-paris7.fr
  • wenliang.li@apc.univ-paris7.fr
  • massimo.taronna@aei.mpg.de

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Issue

Vol. 113, Iss. 9 — 29 August 2014

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