Abstract
In this work we launch a systematic theory of superconformal blocks for fourpoint functions of arbitrary supermultiplets. Our results apply to a large class of superconformal field theories including 4-dimensional models with any number \( \mathcal{N} \) of supersymmetries. The central new ingredient is a universal construction of the relevant Casimir differential equations. In order to find these equations, we model superconformal blocks as functions on the supergroup and pick a distinguished set of coordinates. The latter are chosen so that the superconformal Casimir operator can be written as a perturbation of the Casimir operator for spinning bosonic blocks by a fermionic (nilpotent) term. Solu tions to the associated eigenvalue problem can be obtained through a quantum mechanical perturbation theory that truncates at some finite order so that all results are exact. We illustrate the general theory at the example of d = 1 dimensional theories with \( \mathcal{N} \) = 2 supersymmetry for which we recover known superblocks. The paper concludes with an outlook to 4-dimensional blocks with \( \mathcal{N} \) = 1 supersymmetry.
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Burić, I., Schomerus, V. & Sobko, E. Superconformal blocks: general theory. J. High Energ. Phys. 2020, 159 (2020). https://doi.org/10.1007/JHEP01(2020)159
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DOI: https://doi.org/10.1007/JHEP01(2020)159