All Holographic Four-Point Functions in All Maximally Supersymmetric CFTs

Abstract

We present a constructive derivation of holographic four-point correlators of arbitrary half-BPS operators for all maximally supersymmetric conformal field theories in $d>2$. This includes holographic correlators in 3d $\mathcal{N}=8$ ABJM theories, 4d $\mathcal{N}=4$ SYM theory and the 6d $\mathcal{N}=(2,0)$ theory, dual to tree-level amplitudes in 11D supergravity on $Ad{S}_4\times S^7$, 10D supergravity on $Ad{S}_5\times S^5$ and 11D supergravity on $Ad{S}_7\times S^4$, respectively. We introduce the concept of Maximally R-symmetry Violating (MRV) amplitude, which corresponds to a special configuration in the R-symmetry space. In this limit the amplitude drastically simplifies, but at the same time the entire polar part of the full amplitude can be recovered from this limit. Furthermore, for a specific choice of the polar part, contact terms can be shown to be absent, by using the superconformal Ward identities and the flat space limit.

v1: 31 pages, no figure; v2: minor changes, typos corrected; v3: typos corrected, published on Physical Review X