All Holographic Four-Point Functions in All Maximally Supersymmetric CFTs

TL;DR

This paper derives explicit holographic four-point functions for all maximally supersymmetric conformal field theories in various dimensions, introducing the concept of MRV amplitudes to simplify calculations and recover full correlators.

Contribution

It provides a unified constructive method for all such correlators across different dimensions and introduces MRV amplitudes to streamline the analysis.

Findings

Derived all holographic four-point functions for maximally supersymmetric CFTs.

Introduced the concept of MRV amplitudes to simplify correlator calculations.

Showed how to recover full amplitudes from the MRV limit and identify contact term conditions.

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 ${\cal N}=8$ ABJM theories, 4d ${\cal N}=4$ SYM theory and the 6d ${\cal N}=(2,0)$ theory, dual to tree-level amplitudes in 11D supergravity on $AdS_4 \times S^7$, 10D supergravity on $AdS_5 \times S^5$ and 11D supergravity on $AdS_7 \times S^4$, 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.