Abstract
Using the AdS/CFT correspondence, we study the high-energy behavior of colorless dipole elastic scattering amplitudes in \( \mathcal{N} = 4 \) SYM gauge theory through the Wilson loop correlator formalism and Euclidean to Minkowskian analytic continuation. The purely elastic behavior obtained at large impact-parameter L, through duality from disconnected AdS 5 minimal surfaces beyond the Gross-Ooguri transition point, is combined with unitarity and analyticity constraints in the central region. In this way we obtain an absolute bound on the high-energy behavior of the forward scattering amplitude due to the graviton interaction between minimal surfaces in the bulk. The dominant “Pomeron” intercept is bounded by α ≤ 11=7 using the AdS/CFT constraint of a weak gravitational field in the bulk. Assuming the elastic eikonal approximation in a larger impact-parameter range gives 4/3 ≤ α ≤ 11/7: The actual intercept becomes 4/3 if one assumes the elastic eikonal approximation within its maximally allowed range L ≳ exp Y/3; where Y is the total rapidity. Subleading AdS/CFT contributions at large impact-parameter due to the other d = 10 supergravity fields are obtained. A divergence in the real part of the tachyonic KK scalar is cured by analyticity but signals the need for a theoretical completion of the AdS/CFT scheme.
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Giordano, M., Peschanski, R. High energy bounds on soft \( \mathcal{N} = 4 \) SYM amplitudes from AdS/CFT. J. High Energ. Phys. 2010, 37 (2010). https://doi.org/10.1007/JHEP05(2010)037
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DOI: https://doi.org/10.1007/JHEP05(2010)037