Aspects of Superconformal Multiplets in D>4

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.

arXiv comment118 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

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• Revisiting the classifications of 6d SCFTs and LSTs
• $Ad{S}_6$ T-duals and Type IIB $Ad{S}_6\times S^2$ Geometries with 7-Branes
• Massive spin 2 excitations in $Ad{S}_6\times S^2$ warped spacetimes
• 6d (2,0) and M-theory at 1-loop
• On Mellin Amplitudes in SCFTs with Eight Supercharges
• Universal Bounds on Operator Dimensions from the Average Null Energy Condition
• Holography, Brane Intersections and Six-dimensional SCFTs
• Surface operators in the 6d $\mathcal{N}=(2,0)$ theory
• Superconformal Blocks for SCFTs with Eight Supercharges
• 6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains
• Defect CFT techniques in the 6d $\mathcal{N}=(2,0)$ theory
• Perturbing AdS${}_6{\times }_w{S}^4$: linearised equations and spin-2 spectrum
• Exact Deconstruction of the 6D (2,0) Theory
• 6D (2,0) Bootstrap with soft-Actor-Critic
• More on holographic correlators: Twisted and dimensionally reduced structures
• Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry
• Type-B Anomaly Matching and the 6D (2,0) Theory
• 5d and 6d SCFTs Have No Weak Coupling Limit
• Differential operators for superconformal correlation functions
• Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index
• 3d N=4 Bootstrap and Mirror Symmetry
• Comments on Global Symmetries and Anomalies of $5d$ SCFTs
• Super-Spin Chains for 6D SCFTs
• Bootstrapping (D, D) Conformal Matter
• Non-Lorentzian Avatars of (1,0) Theories
• Superconformal index of higher derivative $\mathcal{N}=1$ multiplets in four dimensions
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories