2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/197441We present a prescription for constructing the monodromy matrix, $\hat{\cal M}(ω)$, for $O(d,d)$ invariant string effective actions and derive its transformation properties under the $T$-duality group. This allows us to construct $\hat{\cal M}(ω)$ 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 $B\neq 0$.6pages, revtex, to be published in Physics Letters BHigh Energy Physics - TheoryExactly Solvable and Integrable Systemstext