| Summary: | 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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