Separation of Variables for a flux tube with an end
We consider a partial light-cone limit of a correlation function of the stress-tensor multiplet and identify an integrable structure emerging at one loop order of perturbation theory. It corresponds to a noncompact open spin chain with one boundary being recoil-less while the other one fully dynamical. We solve the system by means of techniques of the Baxter operator and Separation of Variables. The eigenvalues of separated variables define rapidities of excitations propagating on the color flux tube and encode their factorizable dynamics in the presence of a dynamical boundary.