Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions

Abstract

Abstract:We introduce the impact parameter representation for conformal field theory correlators of the form A ∼ O 1 O 2 O 1 O 2 . This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function O 1 O 1 shock in the presence of a shock wave in Anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch cut, we find the high spin and dimension conformal partial wave decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T -channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high spin O 1 O 2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling.

Analytic bootstrap at large spin

“…Our findings are consistent with AdS/CFT predictions [27][28][29] where it was found that for n 1, γ(n, ) ∝ −n 4 / 2 while for n 1, γ(n, ) ∝ −n 3 / for graviton exchange dominance in the five dimensional bulk.…”

“…of (2.7) is dominated by the exchange of a twist-2 and spin-2 operator exchange. In the language of AdS/CFT, the particle is a graviton that dominates the scattering amplitude in the Eikonal limit [27][28][29]. As in the previous case the anomalous dimension goes as ∼ 1/ 2 for large spin in the r.h.s.…”

“…Recently it has been pointed out that in the context of the AdS/CFT correspondence, there is a connection between the CFT anomalous dimensions and the bulk Shapiro time delay [27][28][29][30]. In [30] it was argued that to preserve causality, the Shapiro time delay should be positive and hence the anomalous dimensions of double trace operators negative.…”

“…In the literature, it has been shown using input from AdS/CFT that using the results for the four point functions of dimension-2 and dimension-3 half-BPS multiplets in N = 4 supersymmetric SU(N ) Yang-Mills theories, to leading order in 1/N 2 , γ(n, ) ≤ 0 for all n -see [31] for a recent calculation for the dimension-2 case and [32] for earlier work related to the dimension-3 case. Furthermore, in [27][28][29], using Eikonal approximation methods pertaining to 2-2 scattering with spin-m exchange in the gravity dual, the anomalous dimensions of largeand large-n operators have been calculated.…”

Deeply virtual Compton scattering from gauge/gravity duality

“…This uses the conformal impact parameter representation introduced in [39] and extensively discussed in [17]. We then compute the hadronic Compton tensor, which is the basic object that allows one to compute the γ * p → γp cross section.…”