Duality and integrability of two-dimensional string effective action

We present a prescription for constructing the monodromy matrix, M(ω), for O(d,d) invariant string effective actions and derive its transformation properties under the T-duality group. This allows us to construct M(ω) for new backgrounds, starting from known ones, which are related by T-duality. As an application, we derive the monodromy matrix for the exactly solvable Nappi–Witten model, both when B=0 and B≠0.