Integrable structures and duality in high-energy QCD

TL;DR

This paper explores the integrable structures underlying high-energy QCD, revealing connections to Seiberg-Witten theory and soliton equations, and discusses the geometric and dynamical implications for Reggeon states, Pomerons, and Odderons.

Contribution

It uncovers the integrable nature of Reggeon states in high-energy QCD and links their spectrum to well-known mathematical structures like Riemann surfaces and Whitham dynamics.

Findings

Identification of integrable Hamiltonian governing Reggeon states

Connection between Baxter equation solutions and Seiberg-Witten theory

Explanation of hyperelliptic Riemann surfaces in QCD context

Abstract

We study the properties of color-singlet Reggeon compound states in multicolor high-energy QCD in four dimensions. Their spectrum is governed by completely integrable (1+1)-dimensional effective QCD Hamiltonian whose diagonalization within the Bethe Ansatz leads to the Baxter equation for the Heisenberg spin magnet. We show that nonlinear WKB solution of the Baxter equation gives rise to the same integrable structures as appeared in the Seiberg-Witten solution for $N=2$ SUSY QCD and in the finite-gap solutions of the soliton equations. We explain the origin of hyperelliptic Riemann surfaces out of QCD in the Regge limit and discuss the meaning of the Whitham dynamics on the moduli space of quantum numbers of the Reggeon compound states, QCD Pomerons and Odderons.