Heisenberg saturation of the Froissart bound from AdS-CFT

In a previous paper, we have analyzed high energy QCD from AdS-CFT and proved the saturation of the Froissart bound (a purely QCD proof of which is still lacking). In this Letter we describe the calculation in more physical terms and map it to QCD language. We find a remarkable agreement with the 1952 Heisenberg description of the saturation (pre-QCD!) in terms of shockwave collisions of pion field distributions. It provides a direct map between gauge theory physics and the gravitational physics on the IR brane of the Randall-Sundrum model. Saturation occurs through black hole production on the IR brane, which is in QCD production of a nonlinear pion field soliton of a Born-Infeld action in the hadron collision, that decays into free pions.