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.
Highlights
Understanding nonperturbative phenomena at strong coupling is one of the most challenging open problems of modern physics
A remarkable relation conjectured by Maldacena, the antide Sitter/conformal field theory (AdS/CFT) correspondence [1,2,3], provides a rare window through which we can gain analytic insight into strongly coupled physics
II A, we review the basic kinematics of four-point functions of one-half BPS operators
Summary
Understanding nonperturbative phenomena at strong coupling is one of the most challenging open problems of modern physics. [48], which introduced superconformal Ward identities (WI) in Mellin space, and it can be applied to any spacetime dimensions This method becomes cumbersome for more general correlators, and only the simplest AdS4 × S7 stress-tensor four-point function was explicitly written down [48]. We develop a unifying method for all three theories by borrowing new ideas from flat-space amplitudes This method leads to a constructive derivation for all tree-level four-point functions with arbitrary conformal dimensions, in all backgrounds with maximal superconformal symmetry. We find a prescription to recover exchange amplitudes from the MRV limit such that no explicit contact terms are present Using this procedure, we construct all tree-level four-point functions in AdS4 × S7, AdS5 × S5, and AdS7 × S4, and write them in a closed-form formula, which exhibits remarkable simplicity.
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