This article provides an in-depth look at hadron high-energy scattering by using gravity dual descriptions of strongly coupled gauge theories. Just like deeply inelastic scattering (DIS) and deeply virtual Compton scattering (DVCS) serve as clean experimental probes into nonperturbative internal structure of hadrons, elastic scattering amplitude of a hadron and a (virtual) photon in gravity dual can be exploited as a theoretical probe. Since the scattering amplitude at sufficiently high energy (small Bjorken $x$) is dominated by parton contributions ($=\mathrm{\text{Pomeron contributions}}$) even in strong coupling regime, there is a chance to learn a lesson for generalized parton distribution (GPD) by using gravity dual models. We begin with refining derivation of the Brower–Polchinski–Strassler–Tan (BPST) Pomeron kernel in gravity dual, paying particular attention to the role played by the complex spin variable $j$. The BPST Pomeron on warped spacetime consists of a Kaluza–Klein tower of 4D Pomerons with nonlinear trajectories, and we clarify the relation between Pomeron couplings and the Pomeron form factor. We emphasize that the saddle-point value $j^{*}$ of the scattering amplitude in the complex $j$-plane representation is a very important concept in understanding qualitative behavior of the scattering amplitude. The total Pomeron contribution to the scattering is decomposed into the saddle-point contribution and at most a finite number of pole contributions, and when the pole contributions are absent (which we call saddle-point phase), kinematical variable $(q,x,t)$-dependence of $\ln (1/q)$ evolution and $\ln (1/x)$ evolution parameters ${\gamma }_{\mathrm{eff}}$ and ${\lambda }_{\mathrm{eff}}$ in DIS and $t$-slope parameter $B$ of DVCS in HERA experiment are all reproduced qualitatively in gravity dual. All of these observations shed a new light on modeling of GPD. Straightforward application of those results to other hadron high-energy scattering is also discussed.

• Received 27 May 2011

DOI:https://doi.org/10.1103/PhysRevD.84.075025