Superconformal blocks: general theory
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 N $$ \mathcal{N} $$ of supersymmetries. The central n...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2020)159 |
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| Summary: | 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 N $$ \mathcal{N} $$ 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 N $$ \mathcal{N} $$ = 2 supersymmetry for which we recover known superblocks. The paper concludes with an outlook to 4-dimensional blocks with N $$ \mathcal{N} $$ = 1 supersymmetry. |
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| ISSN: | 1029-8479 |