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Journal Article

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


Taronna,  Massimo
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Joung, E., Li, W., & Taronna, M. (2014). No-Go Theorems for Unitary and Interacting Partially Massless Spin-Two Fields. Physical Review Letters, 113: 091101. doi:10.1103/PhysRevLett.113.091101.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0019-B9E0-5
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 sign of the PM kinetic term: the former for positive sign and the latter for 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 positive sign. We conclude that there cannot exist a unitary theory of PM spin-two field coupled to Einstein gravity with a perturbatively local Lagrangian. Finally, in the case of negative sign we recover conformal gravity.