Summary: We study exhaustively the solution-generating transformations (dualities) that occur in the context of the low-energy effective action of superstring theory.
We first consider target-space duality (‘T duality’) transformations in the absence of vector fields. We find that for one isometry the full duality group is \((\text{SO}^\uparrow(1, 1))^3\times D_4\), the discrete part \((D_4)\) being non-Abelian. We then include non-Abelian Yang-Mills fields and find the corresponding generalization of the T duality transformations. We study the \(\alpha'\) corrections to these transformations and show that the T duality rules are considerably simplified if the gauge group is embedded in the holonomy group.
Next, in the case in which there are Abelian vector fields, we consider the duality group that includes the transformation, introduced by Sen, that rotates among themselves the components of the metric, axion and vector field.
Finally, we list the duality symmetries of the type II theories with one isometry.