Monodromy, Duality and Integrability of Two Dimensional String Effective Action

In this talk, we show how the monodromy matrix, M̂, can be constructed for the two dimensional tree level string effective action. The pole structure of M̂ is derived using its factorizability property. It is shown that the monodromy matrix transforms non-trivially under the non-compact T-duality group, which leaves the effective action invariant and this can be used to construct the monodromy matrix for more complicated backgrounds starting from simpler ones. We construct, explicitly, M̂ for the exactly solvable Nappi-Witten model, both when B = 0 and B 6= 0, where these ideas can be directly checked.