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

By L. Cornalba, M. Costa, J. Penedones, R. Schiappa. 2006

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We introduce the impact parameter representation for conformal field theory correlators of the form A similar to (O1O2O1O2). 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 (O1O1)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 O1O2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling. (C) 2007 Elsevier B.V. All rights reserved.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/115f563d537d5c0fc09fa43121f54626c521f7ac

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Citations in the corpus

Light-ray operators in conformal field theory (2018, background): “One of the most important is the Regge limit of a time-ordered four-point function (figure 1) [1–6].”
Causality constraints in conformal field theory (2015, methodology): “Our setup differs somewhat from the work of [53, 54] on shockwaves and the eikonal limit in AdS/CFT, in particular we do not assume large N , but ultimately we study a similar limit of the correlator.”
Looking for a bulk point (2015, background): “The relevant limit of the blocks was considered in [16,42-45].”
Universality of long-distance AdS physics from the CFT bootstrap (2014, background): “In perturbative examples [31–33] the anomalous dimension γ(n, `) falls off as a power-law in ` as `→∞ in the case d ≥ 3.”
Witten diagrams revisited: the AdS geometry of conformal blocks (2015, methodology): “crossing symmetry, non-renormalization), and for N = 4 SYM in particular, was performed in [4, 47,52–62].”
A proof of the conformal collider bounds (2016, unknown): “observables such as binding energies [16, 17, 25, 27] and Eikonal phases [73–75] are directly related to the anomalous dimensions of classes of CFT operators with large dimensions and large spin, which are more accessible with the analytic bootstrap methods.”
Bounding the space of holographic CFTs with chaos (2016, methodology): “In general d, the conformal Casimir equation for G∆,s simplifies, admitting a closed-form hypergeometric solution [80] G ∆,s (z, η) = iz G∆,s(η) (3.”
Eikonal approximation in AdS/CFT: from shock waves to four-point functions (2006, unknown): “3.1 General Spin j Interaction 10”
Writing CFT correlation functions as AdS scattering amplitudes (2010, background): “, (6) where 1/N(2) denotes the coupling constant in AdS [12, 13, 14].”
Holography from Conformal Field Theory (2009, background): “[28] that the conformal partial wave expansion of a scalar exchange in AdS only respected (4.”
Stringy effects in scrambling (2014, background): “This arrangement is closely related to the work of [37–39] on high energy scattering in vacuum AdS.”
The analytic bootstrap and AdS superhorizon locality (2012, background): “However, a significant simplification occurs in the limit of very large spin, which is described by the Eikonal limit of 2-to-2 scattering in AdS space, as was worked out in detail in [42, 43].”
Eikonal approximation in AdS/CFT: resumming the gravitational loop expansion (2007, methodology): “ar X iv :0 We derive an eikonal approximation to high energy interactions in Anti–de Sitter spacetime, by generalizing a position space derivation of the eikonal amplitude in flat space.”
Convexity and liberation at large spin (2012, unknown): “2 Different applications of the bootstrap equations in Lorentzian signature were discussed in [28,29,30].”
The conformal bootstrap: Theory, numerical techniques, and applications (2018, background): “(2017a), Costa et al. (2017), Meltzer and Perlmutter (2017), Alday et al.”
Deep inelastic scattering in conformal QCD (2009, methodology): “In this kinematical regime of approximate conformal symmetry, a proposal for restoring unitary of the amplitude was given in [13], based on a conformal phase shift derived from the dual strong coupling picture as a scattering process in AdS space [14–18].”