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The Operator Product Expansion approach to scattering amplitudes in maximallysupersymmetric gauge theory operates in terms of pentagon transitions forexcitations propagating on a color flux tube. These obey a set of axioms whichallow one to determine them to all orders in 't Hooft coupling and confrontagainst explicit calculations. One of the simplifying features of the formalismis the factorizability of multiparticle transitions in terms of single-particleones. In this paper we extend an earlier consideration of a sector populated byone kind of excitations to the case of a system with fermionic as well asbosonic degrees of freedom to address the origin of the factorization. Whilethe purely bosonic case was analyzed within an integrable noncompact open-spinchain model, the current case is solved in the framework of a supersymmetricsl(2|1) magnet. We find the eigenfunctions for the multiparticle system makinguse of the R-matrix approach. Constructing resulting pentagon transitions, weprove their factorized form. The discussion corresponds to leading order ofperturbation theory.

Supersymmetric quantum mechanics of the flux tube