Supersymmetric action for 6D \((4,0)\) supergravity

We give a linearized but otherwise complete supersymmetric action for \({\cal N}=(4,0)\) supergravity in six dimensions, using a Kaluza-Klein-type \(5+1\) split of coordinates and fields. We provide in particular a significantly simplified version of the bosonic action derived by us recently. This formulation employs fields that are no longer irreducible, subject to a local Lorentz invariance, which in turn simplifies the supersymmetry transformations including the exotic gravitino.