  Generalized parton distribution (GPD) contains rich information of partons in
a hadron, including transverse profile, and is also non-perturbative
information necessary in describing a variety of hard processes, such as meson
leptoproduction and double deeply virtual Compton scattering (DDVCS). In order
to unveil non-perturbative aspects of GPD, we study DDVCS at small $x$ in
gravitational dual description. Using the complex spin $j$-plane representation
of DDVCS amplitude, we show that GPD is well-defined and can be extracted from
the amplitude even in the strong coupling regime. It also turns out that the
saddle point value in the $j$-plane representation plays an important role;
there are two phases in the imaginary part of the amplitude of DDVCS and GPD,
depending on relative position of the saddle point and the leading pole in the
$j$-plane, and crossover between them is induced by the change of the
kinematical variables. The saddle point value also directly controls
kinematical variable dependence of many observables in one of the two phases,
and indeed the dependence is qualitatively in nice agreement with HERA
measurements. Such observation that the gravity dual shares basic properties of
the real world QCD suggests that information from BFKL theory might be used to
reduce error in the gravity dual predictions of the form factor and of GPD.
This article also serves as a brief summery of a preprint arXiv:1105.2999.
