Classical integrability of strings in \gamma-deformed backgrounds

This paper considers classical strings propagating in \gamma-deformed AdS_3\times S^3 backgrounds generated by certain shift T-dualities accompanied (TsT) transformations on S^3 and AdS_3, respectively. It finds that the U(1) currents of strings with the twisted boundary conditions are equal to those in \gamma-deformed backgrounds generated by TsT transformations on both S^3 and AdS_3. Applying the TsT transformations, it derives the local Lax connections and the monodromy matrices in \gamma-deformed backgrounds with the spectral parameter which ensure the classical integrability of the string theories.