Abstract
In this paper, we study the general form of three-point functions of conserved current multiplets Sα(k) = S(α1…αk) of arbitrary rank in four-dimensional mathcal{N} = 1 superconformal theory. We find that the correlation function of three such operators leftlangle {overline{S}}_{dot{alpha}(k)}left({z}_1right){S}_{beta left(k+lright)}left({z}_2right){overline{S}}_{dot{gamma}(l)}left({z}_3right)rightrangle is fixed by the superconformal symmetry up to a single complex coefficient though the precise form of the correlator depends on the values of k and l. In addition, we present the general structure of mixed correlators of the form leftlangle {overline{S}}_{dot{alpha}(k)}left({z}_1right){S}_{alpha (k)}left({z}_2right)Lleft({z}_3right)rightrangle and leftlangle {overline{S}}_{dot{alpha}(k)}left({z}_1right){S}_{alpha (k)}left({z}_2right){J}_{gamma dot{gamma}}left({z}_3right)rightrangle , where L is the flavour current multiplet and {J}_{gamma dot{gamma}} is the supercurrent.
Highlights
In this paper, we study the general form of three-point functions of conserved current multiplets Sα(k) = S(α1...αk) of arbitrary rank in four-dimensional N = 1 superconformal theory
We find that the correlation function of three such operators Sα (k)(z1)Sβ(k+l)(z2)Sγ (l)(z3) is fixed by the superconformal symmetry up to a single complex coefficient though the precise form of the correlator depends on the values of k and l
In the non-supersymmetric case, the general structure of the three-point functions of conserved bosonic, vector currents of arbitrary spin was determined by Stanev [37] and Zhiboedov [38], see [39] for similar results in the embedding formalism
Summary
This section contains a concise summary of two and three-point superconformal building blocks in 4D N = 1 superspace, which are important for our subsequent analysis. These superconformal structures were introduced in [14, 15], and later generalised to arbitrary N in [16] (see [19] for a review). A review of the general structure of two- and three-point correlation functions of primary operators is given. The presentation of this section closely follows [51]. Our 4D notation and conventions are those of [50]
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