Eikonal approximation in AdS/CFT: from shock waves to four-point functions

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

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We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function E ∼ hO 1O1i shock in the presence of a shock wave in Anti-de Sitter, where O1 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A ∼ hO 1O2O1O2i , where O2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes.

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

View Paper: https://www.semanticscholar.org/paper/c6ec1fb233edda1a988eccd39a130442bbf26752

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Citations in the corpus

Eikonal approximation in AdS/CFT: resumming the gravitational loop expansion (2007, methodology): “In this work we pursue the program, initiated in [ 1 , 2], of applying eikonal methods in the”
When does the gluon reggeize? (2013, background): “[28, 29]; we do not expect this to modify the analysis in any significant way.”
A bound on chaos (2015, background): “All four point functions of conformal primaries V,W can be computed by analytically continuing the flat space euclidean correlator, with suitable i prescriptions [21, 35].”
Black holes and the butterfly effect (2013, background): “(11)In making the comparison, note that the shift function h in [38] should be identified with twice our shift in v.”
Looking for a bulk point (2015, unknown): “This iε prescription is appropriate when Q lies in the three Poincaré patches nearest Xa [16].”
Entropy production in collisions of gravitational shock waves and of heavy ions (2008, background): “3 Shock waves in anti-de Sitter space Gravitational shock waves are well studied, both in R and AdSD: see for example [36, 37, 38, 39, 40, 41, 42, 43, 44, 45].”
Deep inelastic scattering at strong coupling from gauge/string duality: the saturation line (2007, methodology): “[12, 17 , 18] to deduce the onset of unitarity corrections.”
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].”
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 .”
Spinning AdS propagators (2014, background): “Our expressions can be Wick-rotated to Minkowski signature, provided one is careful with the i prescription (see [24, 25] for some details).”
Stringy effects in scrambling (2014, background): “This arrangement is closely related to the work of [37–39] on high energy scattering in vacuum AdS.”
Light-ray operators in conformal field theory (2018, unknown): “u(∆,J) has a natural analytic continuation in J that is bounded in the right half-plane. This follows from (4.30), since the conformal block G ∆e i J+d−1,∆−d+1(χ,χ) is well-behaved in the square χ,χ∈ [0,1] whenJis in the right half-plane. Let us split the partial wave F∆i ∆,J into two pieces F∆i ∆,J”
A proof of the conformal collider bounds (2016, background): “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.”
Convexity and liberation at large spin (2012, unknown): “2 Different applications of the bootstrap equations in Lorentzian signature were discussed in [28,29,30].”
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.”