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Abstract: This work explores the celebrated AdS-CFT correspondence in the regime ofhigh energy scattering in Anti-de Sitter AdS spacetime. In particular, wedevelop the eikonal approximation to high energy scattering in AdS and exploreits consequences for the dual Conformal Field Theory CFT.Using position space Feynman rules, we rederive the eikonal approximation forhigh energy scattering in flat space. Following this intuitive position spaceperspective, we then generalize the eikonal approximation for high energyscattering in AdS and other spacetimes. Remarkably, we are able to resum, interms of a generalized phase shift, ladder and cross ladder Witten diagramsassociated to the exchange of an AdS spin j field, to all orders in thecoupling constant.By the AdS-CFT correspondence, the eikonal amplitude in AdS is related to thefour point function of CFT primary operators in the regime of large -t Hooftcoupling, including all terms of the 1-N expansion. We then show that theeikonal amplitude determines the behavior of the CFT four point function forsmall values of the cross ratios in a Lorentzian regime and that this controlsits high spin and dimension conformal partial wave decomposition. These resultsallow us to determine the anomalous dimension of high spin and dimension doubletrace primary operators, by relating it to the AdS eikonal phase shift. Finallywe find that, at large energies and large impact parameters in AdS, thegravitational interaction dominates all other interactions, as in flat space.Therefore, the anomalous dimension of double trace operators, associated tograviton exchange in AdS, yields a universal prediction for CFT-s with AdSgravitational duals.

Autor: Joao Penedones Porto University

Fuente: https://arxiv.org/

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