High energy QCD as a completely integrable model

TL;DR

The paper proves that Lipatov's one-dimensional lattice model for high-energy QCD in the large-N limit is completely integrable by identifying it with the XXX Heisenberg magnet at spin s=0 and constructing its commuting local integrals of motion. A generalized Bethe ansatz is developed via a Q-operator and the Baxter equation, enabling the diagonalization of the holomorphic sector and, together with its antiholomorphic counterpart, the full spectral problem; the eigenstates are interpreted in terms of SL(2,C) principal-series representations. For the two-gluon case (BFKL pomeron) the authors recover known results and outline a path to analytic continuation to arbitrary conformal weights h, thereby providing an exact framework for computing high-energy hadron scattering amplitudes in multicolor QCD. This approach clarifies the role of noncompact representations and conformal symmetry in the integrable structure of high-energy QCD interactions.

Abstract

We show that the one-dimensional lattice model proposed by Lipatov to describe the high energy scattering of hadrons in multicolor QCD is completely integrable. We identify this model as the XXX Heisenberg chain of noncompact spin $s=0$ and find the conservation laws of the model. A generalized Bethe ansatz is developed for the diagonalization of the hamiltonian and for the calculation of hadron-hadron scattering amplitude.