On superconformal four-point Mellin amplitudes in dimension d > 2

We present a universal treatment for imposing superconformal constraints on Mellin amplitudes for SCFTd with 3 <= d <= 6. This leads to a new technique to compute holographic correlators, which is similar but complementary to the ones introduced in [1, 2]. We apply this technique to theories in various spacetime dimensions. In addition to reproducing known results, we obtain a simple expression for next-next-to-extremal four-point functions in AdS(7) x S-4. We also use this machinery on AdS(4) x S-7 and compute the first holographic one-half BPS four-point function. We extract the anomalous dimension of the R-symmetry singlet double-trace operator with the lowest conformal dimension and find agreement with the 3d N = 8 numerical bootstrap bound at large central charge.