Implications of N=4 superconformal symmetry in three spacetime dimensions

TL;DR

This paper explores the structure of three-point functions in N=4 superconformal field theories in three dimensions, revealing new tensor structures, relations between correlator coefficients, and explicit calculations in free hypermultiplet models.

Contribution

It extends previous analyses to N=4, identifying two independent structures in supercurrent correlators and deriving universal relations across different N, using Ward identities and superspace methods.

Findings

Two linearly independent structures in supercurrent three-point functions.

Universal relations between correlator coefficients for N=1 to N=4.

Explicit computation of current correlators in free hypermultiplet models.

Abstract

We study implications of N=4 superconformal symmetry in three dimensions, thus extending our earlier results in arXiv:1503.04961 devoted to the N=1,2,3 cases. We show that the three-point function of the supercurrent in 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 N=4 superconformal theories which are not invariant under the mirror map. We point out that general 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 N=4 superconformal models of free hypermultiplets. We also derive the universal relations between the coefficients appearing in the two- and three-point correlators of the supercurrent and flavour current multiplets in all superconformal theories with N=1,2,3,4 supersymmetry. Our derivation is based on the use of Ward identities in conjunction with superspace reduction techniques.