Integrability of high-energy QCD

The high-energy Regge asymptotics of the scattering amplitudes in (3+1)-dim ensional QCD are determined by the properties of color-singlet gluon compou nd states. The spectrum of these states is governed in the multi-color limi t by a completely integrable (1+1)dimensional effective QCD hamiltonian who se diagonalization within the Bethe Ansatz leads to the Baxter equation for the Heisenberg spin magnet. We show that nonlinear WKB solution of the Bax ter equation gives rise to the same integrable structures as appeared in th e Seiberg-Witten solution for N = 2 SUSY QCD and in the finite-gap solution s 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 Whith am dynamics on the moduli space of quantum numbers of the gluon compound st ates.