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.
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ArXiv ePrint: 1701.08163
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Butter, D., Novak, J. & Tartaglino-Mazzucchelli, G. The component structure of conformal supergravity invariants in six dimensions. J. High Energ. Phys. 2017, 133 (2017). https://doi.org/10.1007/JHEP05(2017)133
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DOI: https://doi.org/10.1007/JHEP05(2017)133