Integrable spin chains and scattering amplitudes

In this review, we show that the multi-particle scattering amplitudes in N = 4 SYM 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 complex angular momentum plane of the corresponding t-channel partialwaves. These Mandelstam cuts or Regge cuts result from gluon composite states in the adjoint representation of the gauge group SU(N_c). In the leading logarithmic approximation (LLA), their contribution to the six point amplitude is in full agreement with the known two-loop result. The Hamiltonian for the Mandelstam states constructed from n gluons in LLA coincides with the local Hamiltonian of an integrable open spin chain. We construct the corresponding wavefunctions using the integrals of motion and the BaxterSklyanin approach.