Aspects of Superconformal Multiplets in D>4

TL;DR

Using a unified Verma-module framework, the paper classifies all unitary irreducible representations of the five- and six-dimensional superconformal algebras, computing their spectra and superconformal indices. It applies Racah–Speiser algorithms and Beem–Dolan prescriptions to derive recombination rules, unitarity bounds, and operator constraints, and proves a complete five-dimensional UIR classification via reducibility (Oshima–Yamazaki). The results reveal universal themes across $5$D and $6$D SCFTs, such as non-recombination of higher-spin and stress-tensor multiplets, and provide concrete tools for analyzing spectra, flavor currents, and Schur limits in higher-dimensional theories. The work thereby furnishes detailed multiplet spectra and indices essential for exploring tensor branches, SUSY enhancements, and duality structures in five and six dimensions.

Abstract

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.