Arbitrary $p$-form Galileons

We show that scalar, 0-form, Galileon actions—models whose field equations contain only second derivatives—can be generalized to arbitrary even $p$-forms. More generally, they need not even depend on a single form, but may involve mixed $p$ combinations, including equal $p$ multiplets, where odd $p$ fields are also permitted: We construct, for given dimension $D$, general actions depending on scalars, vectors, and higher $p$-form field strengths, whose field equations are of exactly second derivative order. We also discuss and illustrate their curved-space generalizations, especially the delicate nonminimal couplings required to maintain this order. Concrete examples of pure and mixed actions, field equations, and their curved-space extensions are presented.