Correlation functions and massive Kaluza-Klein modes in the AdS//CFT correspondence

By G. Arutyunov, F. Dolan, H. Osborn, E. Sokatchev. 2002

158 citations recorded by the source corpus.

Abstract We study four-point correlation functions of 1 2 -BPS operators in N =4 SYM which are dual to massive KK modes in AdS5 supergravity. On the field theory side, the procedure of inserting the SYM action yields partial non-renormalisation of the four-point amplitude for such operators. In particular, if the BPS operators have dimensions equal to three or four, the corresponding four-point amplitude is determined by one or two independent functions of the two conformal cross-ratios, respectively. This restriction on the amplitude does not merely follow from the superconformal Ward identities, it also encodes dynamical information related to the structure of the gauge theory Lagrangian. The dimension 3 BPS operator is the AdS/CFT dual of the first non-trivial massive Kaluza–Klein mode of the compactified type IIB supergravity, whose interactions go beyond the level of the five-dimensional gauged N =8 supergravity. We show that the corresponding effective Lagrangian has a surprisingly simple sigma-model-type form with at most two derivatives. We then compute the supergravity-induced four-point amplitude for the dimension 3 operators. Remarkably, this amplitude splits into a “free” and an “interacting” parts in exact agreement with the structure predicted by the insertion procedure. The underlying OPE fulfills the requirements of superconformal symmetry and unitarity.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/52f0522010bb772651509985313c0f9d8d140310

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Witten diagrams revisited: the AdS geometry of conformal blocks (2015, background): “There exists a bevy of identities relating various D∆1∆2∆3∆4(xi) via permutations of the ∆i, spatial derivatives, and/or shifts in the ∆i [18,47].”
All tree-level correlators in AdS5×S5 supergravity: hidden ten-dimensional conformal symmetry (2018, methodology): “[9]), we evaluated these results as functions of z, z̄ variables and compared with H̃ (1) p1p2p3p4 as computed from the action of the differential operator Dp1p2p3p4 on eq.”
How to succeed at holographic correlators without really trying (2017, methodology): “only affects the results for d 6= 5 and thus leaves the conclusions of [23] unaltered.”
A natural language for AdS/CFT correlators (2011, background): “point correlation functions in strongly coupled conformal field theories using supergravity [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], see also [24] for an interesting related conjecture.”
$$ \mathcal{N} $$ = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization (2019, unknown): “(See, for instance, [15–22] for earlier results.”
Loops in AdS from conformal field theory (2016, background): “Even at tree-level, the original calculations [4–13] were impressive but arduous, and struggled to make manifest the relation to CFT data; only recently have leaner, more transparent methods been introduced, including Mellin space [14,15] and geodesic Witten diagrams [16].”
On Four-Point Functions of Half-BPS Operators in General Dimensions (2004, background): “2.1 Conformal cross-ratios and related variables 7 2.2 R symmetry invariant variables 9 2.2.1 The cases SO(5), SO(6) and SO(8) 9 2.2.2 The case SO(3) 10 2.3 Two-, three- and four-point functions 11 2.3.1 Two- and three-point functions 11 2.3.2 Four-point functions 13”
Bounding the space of holographic CFTs with chaos (2016, unknown): “[86]) to write”