Abstract
We consider mathcal{N} = 1 superconformal field theories in four dimensions possessing an additional conserved spinor current multiplet Sα and study three-point functions involving such an operator. A conserved spinor current multiplet naturally exists in superconformal theories with mathcal{N} = 2 supersymmetry and contains the current of the second supersymmetry. However, we do not assume mathcal{N} = 2 supersymmetry. We show that the three-point function of two spinor current multiplets and the mathcal{N} = 1 supercurrent depends on three independent tensor structures and, in general, is not contained in the three-point function of the mathcal{N} = 2 supercurrent. It then follows, based on symmetry considerations only, that the existence of one more Grassmann odd current multiplet in mathcal{N} = 1 superconformal field theory does not necessarily imply mathcal{N} = 2 superconformal symmetry.
Highlights
By Erdmenger and Osborn in [12]
A conserved spinor current multiplet naturally exists in superconformal theories with N = 2 supersymmetry and contains the current of the second supersymmetry
We show that the three-point function of two spinor current multiplets and the N = 1 supercurrent depends on three independent tensor structures and, in general, is not contained in the three-point function of the N = 2 supercurrent
Summary
We provide a brief review of two and three-point superconformal structures in 4D N -extended superspace, which were introduced in [13, 14] in the N = 1 case, and later generalised to arbitrary N in [15] (see [18] for a review). These superconformal structures are important for constructing correlation functions of conserved current multiplets in later sections. This section closely follows [18]
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