New superconformal multiplets and higher derivative invariants in six dimensions

Within the framework of six-dimensional $\mathcal{N}=(1,0)$ conformal supergravity, we introduce new off-shell multiplets $\mathcal{O}{}^{\ast }(n)$, where $n=3,4,\dots ,$ and use them to construct higher-rank extensions of the linear multiplet action. The $\mathcal{O}{}^{\ast }(n)$ multiplets may be viewed as being dual to well-known superconformal $\mathcal{O}(n)$ multiplets. We provide prepotential formulations for the $\mathcal{O}(n)$ and $\mathcal{O}{}^{\ast }(n)$ multiplets coupled to conformal supergravity. For every $\mathcal{O}{}^{\ast }(n)$ multiplet, we construct a higher derivative invariant which is superconformal on arbitrary superconformally flat backgrounds. We also show how our results can be used to construct new higher derivative actions in supergravity.