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arXiv · 0707.0120

Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion

Lorenzo Cornalba·Miguel S. Costa·Joao Penedones
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Abstract

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 < O_1 O_2 O_1 O_2 > 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 ... \partial 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.

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Lorenzo Cornalba, Miguel S. Costa, Joao Penedones. 2007-12-06. Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion. https://doi.org/10.1088/1126-6708%2F2007%2F08%2F019

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