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Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions | | Lorenzo Cornalba
; Miguel S. Costa
; Joao Penedones
; Ricardo Schiappa
; | | Date: |
10 Nov 2006 | | Abstract: | We introduce the impact-parameter representation for conformal field theory correlators of the form A ~ < O_1 O_2 O_1 O_2 >. This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial-wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function < O_1 O_1 >_{shock} in the presence of a shock wave in Anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch-cut, we find the high spin and dimension conformal partial- wave decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high-spin O_1 O_2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling. | | Source: | arXiv, hep-th/0611123 | | Services: | Forum | Review | PDF | Favorites | |
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