Superconformal Blocks for SCFTs with Eight Supercharges

Abstract

We show how to treat the superconformal algebras with eight Poincaré supercharges in a unified manner for spacetime dimension $2<d\le 6$. This formalism is ideally suited for analyzing the quadratic Casimir operator of the superconformal algebra and its use in deriving superconformal blocks. We illustrate this by an explicit construction of the superconformal blocks, for any value of the spacetime dimension, for external protected scalar operators which are the lowest component of flavor current multiplets.

20+9 pages, v2: references added, v3: added closed formulas for the hypermultiplet decomposition

References in corpus (7)

• Bounds on 4D Conformal and Superconformal Field Theories
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Bootstrapping $\mathcal{N}=3$ superconformal theories
• $\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators
• Harmony of Spinning Conformal Blocks

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• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
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• 2d small N=4 Long-multiplet superconformal block
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