On Mellin amplitudes in SCFTs with eight supercharges

A bstract We extend the Mellin space techniques of [1] for computing holographic four-point correlation functions in maximally superconformal theories to theories with only eight Poincaré supercharges. The one-half BPS operators in these correlators are taken to be the superconformal primary in the D k multiplet (with k = 2 corresponding to the flavor current multiplet), and transform in the adjoint representation of a flavor group G . Because of the smaller R-symmetry group SU(2), each individual superconformal Ward identity is less powerful. On the other hand, the constraining power is compensated in number by the different flavor channels in the four-point function. As concrete test cases, we study the Seiberg theories in five dimensions and E-string theory in six dimensions at the large N limit. We show that the flavor current multiplet four-point functions are fixed by superconformal symmetry up to two free parameters, which are proportional to the squared OPE coefficients for the flavor current multiplet and the stress tensor multiplet.