More on holographic correlators: Twisted and dimensionally reduced structures

TL;DR

This paper reveals a hidden dimensional reduction structure in holographic correlators, enabling compact expressions and providing new insights into their properties, with results confirmed by field theory comparisons and predictions for future studies.

Contribution

It uncovers a hidden dimensional reduction in holographic correlators, simplifies their expressions, and connects supergravity results with field theory computations, offering new tools and predictions.

Findings

Correlators exhibit a Parisi-Sourlas type dimensional reduction.

Closed form expressions obtained for $AdS_5\times S^5$ and $AdS_7\times S^4$.

New holographic predictions for OPE coefficients in $AdS_4\times S^7$.

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 \`a 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 $AdS_5\times S^5$ and $AdS_7\times S^4$, 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 $AdS_4\times S^7$, 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.