Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 1, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP01(2020)159
Keywords
Conformal and W Symmetry; Conformal Field Theory; Extended Supersymmetry; Superspaces
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Funding
- ERC [648630 IQFT]
- Knut and Alice Wallenberg foundation
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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 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. Solutions 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 N = 2 supersymmetry for which we recover known superblocks. The paper concludes with an outlook to 4-dimensional blocks with N = 1 supersymmetry.
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