Superconformal blocks: general theory

Burić, Ilija; Sobko, Evgeny; Schomerus, Volker

doi:10.1007/JHEP01(2020)159

Journal Article

PUBDB-2020-00734

Superconformal blocks: general theory

Burić, I.DESY* ; Schomerus, V.DESY* ; Sobko, E. (Corresponding author)

2020
SISSA [Trieste]

Journal of high energy physics 2020(1), 159 (2020) [10.1007/JHEP01(2020)159]

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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

Classification:

ddc:530

Note: JHEP format, an appendix and remarks added, typos corrected

Contributing Institute(s):

Theorie-Gruppe (T)

Research Program(s):

611 - Fundamental Particles and Forces (POF3-611) (POF3-611)

Experiment(s):

No specific instrument

Appears in the scientific report 2020

Database coverage:
Creative Commons Attribution CC BY 4.0

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