Duality symmetry of Reggeon interactions in multicolour QCD

TL;DR

The paper develops a duality symmetry for Reggeon interactions in multicolor QCD by casting the problem as an integral equation for the wavefunction of n reggeized gluons. It leverages holomorphic separability and Möbius invariance to show the Odderon reduces to a $1$-dimensional Schrödinger problem and expresses the full Hamiltonian as a function of a complete set of integrals of motion, with the transfer matrix formalism revealing the underlying integrable structure. A detailed duality equation in the Odderon sector is derived, along with single-valuedness constraints that quantize the spectrum and connect to pseudo-differential and hypergeometric descriptions; the analysis highlights deep links to the Yang-Baxter framework and the XXX spin chain, suggesting a supersymmetric flavor to Reggeon dynamics. These results provide a robust, semi-analytic toolkit for studying high-energy Reggeon exchanges in the large-$N_c$ limit and illuminate the integrable nature of multigluon bound states in QCD.

Abstract

The duality symmetry of the Hamiltonian and integrals of motion for Reggeon interactions in multicolour QCD is formulated as an integral equation for the wave function of compound states of $n$ reggeized gluons. In particular the Odderon problem in QCD is reduced to the solution of the one-dimensional Schrödinger equation. The Odderon Hamiltonian is written in a normal form, which gives a possibility to express it as a function of its integrals of motion.