Integrability of scattering amplitudes in N=4 SUSY

TL;DR

The paper shows that in the planar, large-$N_c$ limit of $\mathcal{N}=4$ SUSY and in multi-Regge kinematics, Mandelstam cuts in the $t$-channel originate from composite states of reggeized gluons in the adjoint representation and can be described by BKP-like equations. In the leading-logarithmic approximation, the holomorphic Hamiltonian governing these adjoint reggeon states coincides with the local Hamiltonian of an integrable open Heisenberg spin chain, enabling construction of the wavefunctions via integrals of motion and the Baxter–Sklyanin method. The authors develop explicit solutions for two- and three-gluon composites and discuss the general structure in terms of holomorphic factorization, integrals of motion, and the Baxter framework, including the role of non-polynomial Baxter functions and the Sklyanin representation. This work bridges high-energy scattering amplitudes in $\mathcal{N}=4$ SUSY with integrable spin-chain techniques, clarifying the analytic structure beyond the BDS ansatz and providing a route toward exact, all-loop insights in the planar limit.

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.