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Journal Article | PUBDB-2020-00734 |
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2020
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Please use a persistent id in citations: doi:10.1007/JHEP01(2020)159 doi:10.3204/PUBDB-2020-00734
Report No.: DESY-19-057; NORDITA 2019-032; arXiv:1904.04852
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.
Keyword(s): operator: Casimir ; field theory: conformal ; quantum mechanics: perturbation theory ; n-point function: 4 ; supersymmetry ; differential equations ; perturbation
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Superconformal Blocks: General Theory
[10.3204/PUBDB-2019-02096]
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