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Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop
Expansion | | Lorenzo Cornalba
; Miguel S. Costa
; Joao Penedones
; | | Date: |
1 Jul 2007 | | 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. | | Source: | arXiv, arxiv.0707.0120 | | Services: | Forum | Review | PDF | Favorites | |
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