Heisenberg saturation of the Froissart bound from AdS-CFT
Kyungsik Kang, Horatiu Nastase
TL;DR
This paper provides a physically transparent bridge between Heisenberg's 1952 saturation of the Froissart bound and modern AdS-CFT descriptions of high-energy QCD. By analyzing scattering in a gravity-dual setup with an IR brane (Randall-Sundrum), the authors show that saturation arises from black-hole/plasma-like soliton formation on the IR brane, yielding a black-disk cross section whose growth matches the Froissart bound. They establish a precise mapping: the lightest gauge-theory excitation (pion or glueball) corresponds to the lightest KK graviton, with the DBI-like action governing the nonlinear dynamics on both sides, explaining why the cross section saturates and how string corrections remain suppressed at high energy. The work thus provides a coherent gauge-gravity mechanism for Froissart saturation and suggests a concrete route toward a purely QCD proof, while preserving a consistent interpretation for both pions and glueballs through the dual description.
Abstract
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 paper 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.