Abstract
We present a constructive derivation of all four-point tree-level holographic correlators for eleven dimensional supergravity on AdS_{7}×S^{4}. These correlators correspond to four-point functions of arbitrary one-half BPS operators in the six-dimensional (2,0) theory at large central charge. The crucial observation is that the polar part of the correlators in Mellin space is fully captured by a drastically simpler maximally R-symmetry violating amplitude, while the contact part is fully fixed by superconformal Ward identities and the flat space limit.
Highlights
Introduction.—Correlators of local operators in holographic conformal field theories (CFTs) are perhaps the most natural observables to test and exploit the AdS=CFT duality
The analogy becomes manifest in Mellin space [1,2], where these methods exploit efficiently the symmetries of the problem and the analytic properties of the Mellin amplitudes
TÞ: We denote this amplitude as maximally R-symmetry violating (MRV), in analogy with MHV amplitudes in flat space
Summary
Invariance under the conformal and R-symmetry group implies that correlators depend only on the invariant cross ratios after a kinematic factor is extracted. We order the weights as k1 ≤ k2 ≤ k3 ≤ k4. It is necessary to distinguish two cases k1 þ k4 ≥ k2 þ k3ðcase IÞ; k1 þ k4 < k2 þ k3ðcase IIÞ: It is useful to define extremality by. The exchanged fields are organized into superconformal multiplets labeled by the Kaluza-Klein level p, where the global symmetry quantum numbers of the relevant component fields are summarized in the table below
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