More on holographic correlators: twisted and dimensionally reduced structures

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 $$ \mathcal{N} $$ 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.

Gluon scattering in AdS from CFT

“…The results in section 4 and 5 exhibit an interesting emergent dimensional Parisi-Sourlaslike reduction structure. A similar structure was observed in correlators in maximally superconformal theories [16]. However, unlike the maximally superconformal situation where the dimension of the AdS space reduces by four, here we find the AdS space dimension reduces only by two.…”

“…This curious dimensional reduction phenomenon turns out to be related to a holographically realized Parisi-Sourlas supersymmetry [35], and is a feature shared by all the AdS supersymmetric gauge theories considered in this paper. Similar dimensional reduction was observed in maximally supersymmetric super graviton amplitudes [16]. However, in that case the dimension of the AdS space is reduced by four instead of two.…”

“…In [16], the modified R-symmetry dependence was shown to be related to reducing the dimension of the internal sphere also by four. However, it is less clear here how to geometrically interpret Y p,ν , as the factorization into SU(2) R × SU(2) L is a feature of S 3 only and the SU(2) L factor is left intact throughout.…”

“…This computation can be done by examining kkqq correlators (and their permutations), from which we can also extract all three-point functions for super primary operators. 16 Let us expand on this point. We first look at the 22qq correlators and consider the following ratios λ…”

“…This property, however, is not shared by super graviton amplitudes in 11d supergravity compactified on AdS 4 × S 7 and AdS 7 × S 4 . Another independent dimensional reduction structure was recently discovered in [16], which allows all super graviton amplitudes to be expressed in terms of the amplitudes of a simple scalar seed theory in lower dimensions. This emergent structure is universal to all maximally supersymmetric theories, and appears to be closely related to the Parisi-Sourlas supersymmetry [17].…”