The component structure of conformal supergravity invariants in six dimensions

Abstract

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.

42 pages; supplementary file included in submission; v2: added references, corrected typos; v3: minor corrections, references added

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