Spectrum-generating symmetries for BPS solitons

We show that there exist non-linearly realised duality symmetries that are independent of the standard supergravity global symmetries, and which provide active spectrum-generating symmetries for the fundamental BPS solitons. The additional ingredient, in any space-time dimension, is a single scaling transformation that allows one to map between BPS solitons with different masses. Without the inclusion of this additional transformation, which is a symmetry of the classical equations of motion, but not the action, it is not possible to find a spectrum-generating symmetry. The necessity of including this scaling transformation highlights the vulnerability of duality multiplets to quantum anomalies. We argue that fundamental BPS solitons may be immune to this threat. (orig.)