Cubic interactions for massless and partially massless spin-1 and spin-2 fields

Understand

We perform a complete classification of the consistent two-derivative cubic couplings for a system containing an arbitrary number of massless spin-1, massless spin-2, and partially massless (PM) spin-2 fields in $D$-dimensional (anti-)de Sitter space.

• In addition to previously known results, we find a unique candidate mixing between spin-1 and PM spin-2 fields.
• We derive all the quadratic constraints on the structure constants of the theory, allowing for relative ``wrong-sign'' kinetic terms for any of the fields.
• In the particular case when the kinetic terms in each sector have no relative signs, we find that the unique consistent non-trivial theory is given by multiple independent copies of conformal gravity coupled to a Yang-Mills sector in $D=4$.