Abstract
In the recent paper arXiv:1606.02921 , the two invariant actions for 6D N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ conformal supergravity were constructed in superspace, corresponding to the supersymmetrization of C3 and C□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□F action coupled to conformal supergravity. Exploiting the fact that the N = 2 0 $$ \mathcal{N}=\left(2,0\right) $$ Weyl multiplet has a consistent truncation to N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ , we then verify that there is indeed only a single N = 2 0 $$ \mathcal{N}=\left(2,0\right) $$ conformal supergravity invariant and reconstruct most of its bosonic terms by uplifting a certain linear combination of N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ invariants.