  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.
