Abstract
We review the theory for a multiplet of interacting partially massless spin-2 fields around (anti-) de Sitter (A)dS\(_{D}\) background and give new results concerning the couplings between a massless spin-1 vector field and a partially massless spin-2 field.
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Notes
We allow for the study of classically non-unitary theories. Actually, PM fields can be defined around AdS\(_{D}\) where they are non-unitary. This can be seen explicitly by writing the action, which is real for both signs of the cosmological constant, in the Stueckelberg formulation [8].
Here \(t.d. = {{\partial }_{\mu }}{{j}^{\mu }}\) for some vector \({{j}^{\mu }}\). Since one can always rewrite \({{j}^{\mu }} = \sqrt { - \bar {g}} \mathop {\tilde {j}}\nolimits^\mu \) this implies \({{\partial }_{\mu }}{{j}^{\mu }} = \sqrt { - \bar {g}} {{\nabla }_{\mu }}\mathop {\tilde {j}}\nolimits^\mu \) and \(t.d.\) represents up to a \(\sqrt { - \bar {g}} \) factor a total derivative using a Lorentz-covariant derivative of the background. We will thus always write \(t.d.\) although this can mean \({{\partial }_{\mu }}{{j}^{\mu }}\) or \({{\nabla }_{\mu }}{{j}^{\mu }}\) depending on the context.
Note that allowing for more derivatives we can trivially construct Born–Infeld type vertices; they contain at least three derivatives and do not deform the gauge transformation laws of the free theory.
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Boulanger, N., Garcia-Saenz, S. & Traina, L. Interactions for Partially-Massless Spin-2 Fields. Phys. Part. Nuclei Lett. 17, 687–691 (2020). https://doi.org/10.1134/S1547477120050064
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DOI: https://doi.org/10.1134/S1547477120050064