Pseudo-Duality

Proper symmetries act on fields while pseudo-symmetries act on both fields and coupling constants. We identify the pseudo-duality groups that act as symmetries of the equations of motion of general systems of scalar and vector fields and apply our results to $N=2,4$ and $8$ supergravity theories. We present evidence that the pseudo-duality group for both the heterotic and type II strings toroidally compactified to four dimensions is $Sp(56;\Z)\times D$, where $D$ is a certain subgroup of the diffeomorphism group of the scalar field target space. This contains the conjectured heterotic $S\times T$ or type II $U$ proper duality group as a subgroup.