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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
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 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.
