The component structure of conformal supergravity invariants in six dimensions

In the recent paper arXiv : 1606.02921, the two invariant actions for 6D N = (1; 0) conformal supergravity were constructed in superspace, corresponding to the supersymmetrization of C-3 and C square C. In this paper, we provide the translation from superspace to the component formulation of superconformal tensor calculus, and we give the full component actions of these two invariants. As a second application, we build the component form for the supersymmetric F square F action coupled to conformal supergravity. Exploiting the fact that the N = (2; 0) Weyl multiplet has a consistent truncation to N = (1; 0), we then verify that there is indeed only a single N = (2; 0) conformal supergravity invariant and reconstruct most of its bosonic terms by uplifting a certain linear combination of N = (1; 0) invariants.