Integrability of scattering amplitudes in N=4 SUSY

TL;DR

This paper demonstrates that multi-particle scattering amplitudes in N=4 SUSY exhibit integrable structures, with the high energy behavior linked to Mandelstam cuts and gluon composite states, modeled by an integrable open spin chain.

Contribution

It establishes the integrability of the Hamiltonian for gluon states in N=4 SUSY scattering amplitudes using the Baxter-Sklyanin approach.

Findings

High energy behavior from Mandelstam cuts in N=4 SUSY

Hamiltonian matches that of an integrable open spin chain

Wave functions constructed via integrals of motion

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.