Skewness dependence of generalized parton distributions, conformal OPE, and the AdS/CFT correspondence

Abstract

The traditional idea of the Pomeron/Reggeon description for hadron scattering is now being given theoretical foundation in gravity dual descriptions, where Pomeron corresponds to an exchange of spin-$j\ensuremath{\in}2\mathbb{Z}$ states in the graviton trajectory. Deeply virtual Compton scattering (DVCS) is essentially a two-to-two scattering process of a hadron and a photon, and hence one should be able to study nonperturbative aspects (the generalized parton distribution [GPD]) of this process by the Pomeron/Reggeon process in gravity dual. We find, however, that even one of the most developed formulations of gravity dual, Pomeron [Brower-Polchinski-Strassler-Tan (BPST), 2006], is not able to capture skewness dependence of GPD properly. Therefore, we compute Reggeon wave functions on ${\mathrm{AdS}}_{5}$ so that the formalism of BPST can be generalized. These wave functions are used to determine the DVCS amplitude, bring it to the form of conformal operator product expansion/collinear factorization, and extract a holographic model of GPD, which naturally fits into the framework known as ``dual parametrization,'' or the ``(conformal) collinear factorization approach.''