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.
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ArXiv ePrint: 1507.00221
Dedicated to the memory of Professor Boris M. Zupnik
On leave from Tomsk Polytechnic University, 634050 Tomsk, Russia. (Igor B. Samsonov)
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Buchbinder, E.I., Kuzenko, S.M. & Samsonov, I.B. Implications of \( \mathcal{N}=4 \) superconformal symmetry in three spacetime dimensions. J. High Energ. Phys. 2015, 125 (2015). https://doi.org/10.1007/JHEP08(2015)125
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DOI: https://doi.org/10.1007/JHEP08(2015)125