The component structure of conformal supergravity invariants in six dimensions

Abstract

In the recent paper arXiv:1606.02921, the two invariant actions for 6D $\mathcal{N}=\left(1,0\right)$ conformal supergravity were constructed in superspace, corresponding to the supersymmetrization of C ³ 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 $\mathcal{N}=\left(2,0\right)$ Weyl multiplet has a consistent truncation to $\mathcal{N}=\left(1,0\right)$, we then verify that there is indeed only a single $\mathcal{N}=\left(2,0\right)$ conformal supergravity invariant and reconstruct most of its bosonic terms by uplifting a certain linear combination of $\mathcal{N}=\left(1,0\right)$ invariants.