No-Go Theorems for Unitary and Interacting Partially Massless Spin-Two Fields
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.
Cite
@article{arxiv.1406.2335,
title = {No-Go Theorems for Unitary and Interacting Partially Massless Spin-Two Fields},
author = {Euihun Joung and Wenliang Li and Massimo Taronna},
journal= {arXiv preprint arXiv:1406.2335},
year = {2014}
}
Comments
20 pages, LaTex, v2: references added, typos corrected; discussion added about the pure PM theory without massless spin-2 field; extended version of the letter accepted in PRL