Implications of N = 4 $$ \mathcal{N}=4 $$ superconformal symmetry in three spacetime dimensions

Abstract

We study implications of $$ \mathcal{N}=4 $$ superconformal symmetry in three dimensions, thus extending our earlier results in [1] devoted to the $$ \mathcal{N}\le 3 $$ cases. We show that the three-point function of the supercurrent in $$ \mathcal{N}=4 $$ superconformal field theories contains two linearly independent forms. However, only one of these structures contributes to the three-point function of the energy-momentum tensor and the other one is present in those $$ \mathcal{N}=4 $$ superconformal theories which are not invariant under the mirror map. We point out that general $$ \mathcal{N}=4 $$ superconformal field theories admit two inequivalent flavour current multiplets and show that the three-point function of each of them is determined by one tensor structure. As an example, we compute the two- and three-point functions of the conserved currents in $$ \mathcal{N}=4 $$ superconformal models of free hypermultiplets. We also derive the universal relations between the coefficients appearing in the two- and threepoint correlators of the supercurrent and flavour current multiplets in all superconformal theories with $$ \mathcal{N}\le 4 $$ supersymmetry. Our derivation is based on the use of Ward identities in conjunction with superspace reduction techniques.