Aspects of Superconformal Multiplets in D>4

We explicitly construct and list all unitary superconformal multiplets, along with their index contributions, in five and six dimensions. From this data, we uncover various unifying themes in the representation theory of five- and six-dimensional superconformal field theories. At the same time, we provide a detailed argument for the complete classification of unitary irreducible representations in five dimensions using a combination of physical and mathematical techniques.
Comment: 118 pages; v2 typos corrected and references added ; v3 classification of 5D unitary multiplets corrected and C-type multiplets removed ; v4 discussion of the procedure for obtaining irreps of the SCA improved and typos corrected, published version