In 1981, Gaillard and Zumino studied a broad class of models — including axiverse models and several extended supergravities as special cases — whose equations of motion are classically invariant under continuous symplectic transformations acting on the gauge sector. The standard lore holds that, at the quantum level, these symmetries are broken to an integral subgroup, usually identified with the U-duality group. I will argue that, in fact, a much larger subgroup of rational symplectic transformations can be associated with quantum symmetries, albeit realized through non-invertible topological defects, and I will discuss some of their implications.