Journal of High Energy Physics (Jul 2021)

Correlation functions of spinor current multiplets in N $$ \mathcal{N} $$ = 1 superconformal theory

  • Evgeny I. Buchbinder,
  • Jessica Hutomo,
  • Sergei M. Kuzenko

DOI
https://doi.org/10.1007/JHEP07(2021)165
Journal volume & issue
Vol. 2021, no. 7
pp. 1 – 36

Abstract

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Abstract We consider N $$ \mathcal{N} $$ = 1 superconformal field theories in four dimensions possessing an additional conserved spinor current multiplet S α and study three-point functions involving such an operator. A conserved spinor current multiplet naturally exists in superconformal theories with N $$ \mathcal{N} $$ = 2 supersymmetry and contains the current of the second supersymmetry. However, we do not assume N $$ \mathcal{N} $$ = 2 supersymmetry. We show that the three-point function of two spinor current multiplets and the N $$ \mathcal{N} $$ = 1 supercurrent depends on three independent tensor structures and, in general, is not contained in the three-point function of the N $$ \mathcal{N} $$ = 2 supercurrent. It then follows, based on symmetry considerations only, that the existence of one more Grassmann odd current multiplet in N $$ \mathcal{N} $$ = 1 superconformal field theory does not necessarily imply N $$ \mathcal{N} $$ = 2 superconformal symmetry.

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