Integrability of scattering amplitudes in N=4 SUSY

Abstract

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.

25 pages, no figures

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