Solving Superconformal Ward Identities in Mellin Space

We study four-point correlators in superconformal theories in various dimensions. We develop an efficient method to solve the superconformal Ward identities in Mellin space. For 4d $\mathcal{N}=4$ SYM and the 6d $\mathcal{N}=(2,0)$ theory, our method reproduces the known solutions. As novel applications of this method, we also derive solutions in 3d $\mathcal{N}=8$ ABJM, and in 4d $\mathcal{N}=4$ SYM with line defects.