Integrable spin chains and scattering amplitudes

TL;DR

This paper reviews how multi-particle scattering amplitudes in N=4 SYM relate to integrable spin chains and Mandelstam cuts, providing insights into high-energy behavior and gluon states.

Contribution

It demonstrates the connection between Mandelstam cuts in scattering amplitudes and integrable open spin chains, offering a new perspective on high-energy QCD processes.

Findings

Mandelstam cuts arise from gluon composite states in the adjoint representation.

The Hamiltonian for Mandelstam states matches that of an integrable open spin chain.

Wave functions are constructed using integrals of motion and Baxter-Sklyanin approach.

Abstract

In this review we show that the multi-particle scattering amplitudes in N=4 SYM at large Nc 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 partial waves. These Mandelstam cuts or Regge cuts are resulting from gluon composite states in the adjoint representation of the gauge group SU(Nc). 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 wave functions using the integrals of motion and the Baxter-Sklyanin approach.