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Eikonal Approach to N=4 SYM Regge Amplitudes in the AdS/CFT Correspondence

The high-energy behavior of N=4 SYM elastic amplitudes at strong coupling is studied by means of the AdS/CFT correspondence. We consider the eikonal method proposed by Janik and one of the authors, where the relevant minimal surface is a "generalized helicoid" in hyperbolic space ("Euclidean AdS_5"), from which the physical amplitude is obtained after an appropriate analytic continuation. We then compare our results with those obtained, using a minimal surface in AdS_5 momentum space, by Alday and Maldacena for gluon-gluon scattering, and by Barnes and Vaman for quark-quark scattering ("Alday-Maldacena approach"). Exploiting a conformal transformation, we show that the eikonal amplitudes are dominated by the Euclidean version of the cusp contribution found in the Alday-Maldacena approach. The amplitudes in the two approaches are of Regge type at high-energy and with the same logarithmic Regge trajectory independently of the kind of colliding particles, in agreement with the expected universality of Regge trajectories.