Abstract
Recently four-point holographic correlators with arbitrary external BPS operators were constructively derived in [1, 2] at tree-level for maximally superconformal theories. In this paper, we capitalize on these theoretical data, and perform a detailed study of their analytic properties. We point out that these maximally supersymmetric holographic correlators exhibit a hidden dimensional reduction structure à la Parisi and Sourlas. This emergent structure allows the correlators to be compactly expressed in terms of only scalar exchange diagrams in a dimensionally reduced spacetime, where formally both the AdS and the sphere factors have four dimensions less. We also demonstrate the superconformal properties of holographic correlators under the chiral algebra and topological twistings. For AdS5× S5 and AdS7× S4, we obtain closed form expressions for the meromorphic twisted correlators from the maximally R-symmetry violating limit of the holographic correlators. The results are compared with independent field theory computations in 4d mathcal{N} = 4 SYM and the 6d (2, 0) theory, finding perfect agreement. For AdS4× S7, we focus on an infinite family of near-extremal four-point correlators, and extract various protected OPE coefficients from supergravity. These OPE coefficients provide new holographic predictions to be matched by future supersymmetric localization calculations. In deriving these results, we also develop many technical tools which should have broader applicability beyond studying holographic correlators.
Highlights
The holographic computation of superconformal correlators using AdS supergravity has been an extremely difficult task, even just at tree-level and for four half-BPS operators
We focus on the supergravity backgrounds AdS4 ×S7, AdS5 ×S5 and AdS7 ×S4, which have the maximal amount of superconformal symmetry
The full higher-spin algebra is known: it is the quantization of the classical WN algebra, 13The R-symmetry decomposes as su(2) × u(1) ⊂ usp(4) and all operators that can contribute to the chiral algebra are neutral under u(1)
Summary
The holographic computation of superconformal correlators using AdS supergravity has been an extremely difficult task, even just at tree-level and for four half-BPS operators (see, e.g., [3,4,5,6,7] for early progress). The full correlators are reconstructed from this limit by using symmetries This method applies to any spacetime dimension, and leads to a closed form formula for all tree-level four-point functions in all maximally supersymmetric theories [1, 2]. We will point out a different hidden structure in tree-level four-point functions that involves dimensional reduction, and is present in all maximally superconformal theories. Given that many aspects of the protected subsectors appear to be within reach of a formal proof, it might be helpful to turn the logic around and view our results as a tree-level check of AdS/CFT In performing these checks, we have developed many technical tools for studying holographic four-point functions.
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