On The Pomeron at Large 't Hooft Coupling

TL;DR

This paper develops a holographic approach to unitarize high-energy scattering by summing multi-Pomeron exchanges in the large-$\lambda$ regime. By transforming the Pomeron kernel to the $J$-plane and transverse space, the authors derive an AdS$_5$ eikonal framework in which the single-Pomeron exchange kernel reduces to an $AdS_3$ scalar propagator, yielding a phase and absorptive part that encode elastic and inelastic processes. The work shows that in the conformal case the eikonal sum respects bulk unitarity and naturally extends to confining theories, where the Froissart bound is both satisfied and saturated with a $(\log s)^2$ growth, governed by the lightest spin-2 glueballs. The analysis highlights a multi-channel interpretation via KK modes, a string-bit picture in flat space, and a smooth interpolation to graviton exchange as $\lambda \to \infty$. Overall, the framework provides a concrete, calculable path toward Gribov–Regge effective theory in the strong-coupling limit and offers insights for QCD-like Pomeron dynamics.

Abstract

We begin the process of unitarizing the Pomeron at large 't Hooft coupling. We do so first in the conformal regime, which applies to good accuracy to a number of real and toy problems in QCD. We rewrite the conformal Pomeron in the $J$-plane and transverse position space, and then work out the eikonal approximation to multiple Pomeron exchange. This is done in the context of a more general treatment of the complex $J$-plane and the geometric consequences of conformal invariance. The methods required are direct generalizations of our previous work on single Pomeron exchange and on multiple graviton exchange in AdS space, and should form a starting point for other investigations. We consider unitarity and saturation in the conformal regime, noting elastic and absorptive effects, and exploring where different processes dominate. Our methods extend to confining theories and we briefly consider the Pomeron kernel in this context. Though there is important model dependence that requires detailed consideration, the eikonal approximation indicates that the Froissart bound is generically both satisfied and saturated.

Figures (7)

• Figure 1: Schematic form of the $\Delta-j$ relation for $\lambda\ll 1$ and $\lambda\gg 1$. The dashed lines show the $\lambda =0$ DGLAP branch (slope 1), BFKL branch (slope 0), and inverted DGLAP branch (slope $-1$). Note that the curves pass through the points (4,2) and (0,2) where the anomalous dimension must vanish. This curve is often plotted in terms of $\Delta - j$ instead of $\Delta$, but this obscures the inversion symmetry $\Delta \to 4-\Delta$.
• Figure 2: The function $G_3(j,v)$ for $j=j_0$ (the solid line for the Pomeron, with $\Delta=2$) and for $j=2$ (the dashed line for the graviton, with $\Delta=4$). Note $G_3(j,v)\sim 1/\sqrt v$ for $v\ll 1$ and $\sim v^{1-\Delta_+(j)}$ for $v\gg 1$. Thus the two functions have the same small-$v$ behavior, but the graviton falls off faster than the Pomeron.
• Figure 3: Ladder and crossed ladder diagrams contributing to the eikonal approximation in the high energy limit.
• Figure 4: Sum of box and crossed box diagrams is factorized with combinatoric weight $1/2!$.
• Figure 5: Reggeon particle scattering amplitude in the planar approximation, $A_{13}(M^2,t)$, with $t = (q_1 + q_2)^2$ and $M^2 = (p_1 + q_1)^2$.