Eikonal approximation in AdS/CFT: resumming the gravitational loop expansion

By L. Cornalba, M. Costa, J. Penedones. 2007

204 citations recorded by the source corpus.

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. We are able to resum, in terms of a generalized phase shift, ladder and cross ladder graphs associated to the exchange of a spin j field, to all orders in the coupling constant. Using the AdS/CFT correspondence, the resulting amplitude determines the behavior of the dual conformal field theory four-point function for small values of the cross ratios, in a Lorentzian regime. Finally we show that the phase shift is dominated by graviton exchange and computes, in the dual CFT, the anomalous dimension of the double trace primary operators O-1 partial derivative...partial derivative O-2 of large dimension and spin, corresponding to the relative motion of the two interacting particles. The results are valid at strong t'Hooft coupling and are exact in the 1/N expansion.

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

View Paper: https://www.semanticscholar.org/paper/1037c319477532a155bbfe4f8470322721f8a748

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Citations in the corpus

Looking for a bulk point (2015, background): “The relevant limit of the blocks was considered in [16,42-45].”
Writing CFT correlation functions as AdS scattering amplitudes (2010, background): “However, it is not clear that this controls the Regge limit of the four point function as defined in [27, 28, 29, 20].”
Gravitational S-matrix from CFT dispersion relations (2017, background): “f large scaling dimension, where the CFT-data is expected to encode the scattering amplitude of a pair of excitations with large center-of-mass energy in AdS units p sL= 2n, through a simple relation [2,14] (discussed further in section5): lim n!1 ae iˇ n;‘ a(0) n;‘ = b ‘(s): (2.15) { 5 { = P single”
Convexity and liberation at large spin (2012, unknown): “2 Different applications of the bootstrap equations in Lorentzian signature were discussed in [28,29,30].”
Effective conformal theory and the flat-space limit of AdS (2010, unknown): “[5, 6, 31, 32, 9, 33, 13, 14]), but extracting information about anomalous”
Stringy effects in scrambling (2014, background): “It has also been studied in pure AdS by [39, 44].”
Spinning AdS propagators (2014, background): “In fact, we can think of γ(n, l) as the gravitational binding energy of a two particle state with angular momentum l [51].”
Causality constraints on corrections to the graviton three-point coupling (2014, background): “This question was addressed in a nice series of papers [58, 63, 64] where the time delay was shown to be equal to anomalous dimension of double trace operators of the type O(∂(2))∂μ1 .”
Loops in AdS from conformal field theory (2016, background): “While there is some work on one-loop AdS amplitudes [15,25–27], some of which we will make contact with later, loop physics in AdS has mostly been studied using other simpler observables, specifically the partition function (e.”
Holography from Conformal Field Theory (2009, background): “This configuration of the cross ratios can be obtained as an analytic continuation of the Euclidean amplitude [34].”
An algebraic approach to the analytic bootstrap (2015, background): “Taking into accounts the descendants and considering n 1 limit we expect to recover the full AdS propagator along the lines of [25].”
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].”
Deep inelastic scattering in conformal QCD (2009, background): “In this regime, unitarity is recovered by including multiple graviton exchanges in the eikonal approximation [16,17].”
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.”