O(2,2) transformations and the string Geroch group

The 1-loop string background equations with axion and dilaton fields are shown to be integrable in four dimensions in the presence of two commuting Killing symmetries and $\delta c = 0$. Then, in analogy with reduced gravity, there is an infinite group that acts on the space of solutions and generates non-trivial string backgrounds from flat space. The usual $O(2,2)$ and $S$-duality transformations are just special cases of the string Geroch group, which is infinitesimally identified with the $O(2,2)$ current algebra. We also find an additional $Z_{2}$ symmetry interchanging the field content of the dimensionally reduced string equations. The method for constructing multi-soliton solutions on a given string background is briefly discussed.