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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| Format: | Article |
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SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2020)159 |
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| author | Ilija Burić Volker Schomerus Evgeny Sobko |
| author_facet | Ilija Burić Volker Schomerus Evgeny Sobko |
| author_sort | Ilija Burić |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a44df8fa12c047ad870f897a51a6a610 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-a44df8fa12c047ad870f897a51a6a6102025-02-09T12:06:20ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020114110.1007/JHEP01(2020)159Superconformal blocks: general theoryIlija Burić0Volker Schomerus1Evgeny Sobko2Deutsches Elektronen-Synchrotron (DESY)Deutsches Elektronen-Synchrotron (DESY)School of Phyffics and Astronomy, University of SouthamptonAbstract 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.https://doi.org/10.1007/JHEP01(2020)159Conformal and W SymmetryConformal Field TheoryExtended SupersymmetrySuperspaces |
| spellingShingle | Ilija Burić Volker Schomerus Evgeny Sobko Superconformal blocks: general theory Journal of High Energy Physics Conformal and W Symmetry Conformal Field Theory Extended Supersymmetry Superspaces |
| title | Superconformal blocks: general theory |
| title_full | Superconformal blocks: general theory |
| title_fullStr | Superconformal blocks: general theory |
| title_full_unstemmed | Superconformal blocks: general theory |
| title_short | Superconformal blocks: general theory |
| title_sort | superconformal blocks general theory |
| topic | Conformal and W Symmetry Conformal Field Theory Extended Supersymmetry Superspaces |
| url | https://doi.org/10.1007/JHEP01(2020)159 |
| work_keys_str_mv | AT ilijaburic superconformalblocksgeneraltheory AT volkerschomerus superconformalblocksgeneraltheory AT evgenysobko superconformalblocksgeneraltheory |