Holographic Four-Point Functions in the (2, 0) Theory

We revisit the calculation of holographic correlators for eleven-dimensional supergravity on $Ad{S}_7\times S^4$. Our methods rely entirely on symmetry and eschew detailed knowledge of the supergravity effective action. By an extension of the position space approach developed in [1, 2] for the $Ad{S}_5\times S^5$ background, we compute four-point correlators of one-half BPS operators for identical weights $k=2,3,4$. The $k=2$ case corresponds to the four-point function of the stress-tensor multiplet, which was already known, while the other two cases are new. We also translate the problem in Mellin space, where the solution of the superconformal Ward identity takes a surprisingly simple form. We formulate an algebraic problem, whose (conjecturally unique) solution corresponds to the general one-half BPS four-point function.