  We argue, that the multi-particle scattering amplitudes in N=4 SUSY at large
$N_c$ and in the multi-Regge kinematics for some physical regions have the high
energy behavior appearing from the contribution of the Mandelstam cuts in the
corresponding $t$-channel partial waves. The Mandelstam cuts correspond to
gluon composite states in the adjoint representation of the gauge group
$SU(N_c)$. The hamiltonian for these states in the leading logarithmic
approximation coincides with the local hamiltonian of an integrable open spin
chain. We construct the corresponding wave functions using the integrals of
motion and the Baxter-Sklyanin approach.
