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Abstract
We develop a general formalism to study the threepoint correlation functions of conserved higherspin supercurrent multiplets J𝜶(r)̇𝜶(r) in 4D N=1 superconformal theory. All the constraints imposed by N=1 superconformal symmetry on the threepoint function ⟨J𝜶(r_{1})̇𝜶(r_{1})J𝜷(r_{2})̇𝜷(r_{2})J𝜸(r_{3})̇𝜸(r_{3})⟩ are systematically derived for arbitrary r_{1},r_{2},r_{3}, thus reducing the problem mostly to computational and combinatorial. As an illustrative example, we explicitly work out the allowed tensor structures contained in ⟨J𝜶(r)̇𝜶(r)J𝜷̇𝜷J𝜸̇𝜸⟩, where J𝜶̇𝜶 is the supercurrent. We find that this threepoint function depends on two independent tensor structures, though the precise form of the correlator depends on whether r is even or odd. The case r=1 reproduces the threepoint function of the ordinary supercurrent derived by Osborn. Additionally, we present the most general structure of mixed correlators of the form ⟨LLJ𝜶(r)̇𝜶(r)⟩and ⟨J𝜶(r_{1})̇𝜶(r_{1})J𝜷(r_{2})̇𝜷(r_{2})L⟩, where L is the flavour current multiplet.
Original language  English 

Article number  2200133 
Number of pages  23 
Journal  Fortschritte der Physik 
Volume  70 
Issue number  12 
Early online date  27 Sept 2022 
DOIs  
Publication status  Published  Dec 2022 
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Advances in Conformal Field Theory with Extended Symmetry
Kuzenko, S., Buchbinder, E., Theisen, S. & Tseytlin, A.
ARC Australian Research Council
1/01/20 → 31/12/23
Project: Research

Supersymmetry and Supergravity: New Approaches and Applications
TartaglinoMazzucchelli, G.
ARC Australian Research Council
1/01/18 → 9/10/20
Project: Research